Added Appendix with calculation of modulus with higher-order interaction, made figure bigger.

1 files changed, 50 insertions, 47 deletions

diff --git a/hidden_order.bib b/hidden_order.bib
index b3b6e38..e2ed334 100644
--- a/hidden_order.bib
+++ b/hidden_order.bib
@@ -86,7 +86,7 @@ Ultrasound Spectroscopy and Machine Learning},
  isbn = {9780511813467}
 }
 
-@article{Chandra_2013a,
+@article{Chandra_2013_Hastatic,
  author = {Chandra, Premala and Coleman, Piers and Flint, Rebecca},
  title = {Hastatic order in the heavy-fermion compound {URu$_2$Si$_2$}},
  journal = {Nature},
@@ -100,13 +100,13 @@ Ultrasound Spectroscopy and Machine Learning},
  doi = {10.1038/nature11820}
 }
 
-@article{Chandra_2013b,
+@article{Chandra_2013_Origin,
  author = {Chandra, Premala and Coleman, Piers and Flint, Rebecca},
- title = {Origin of the Large Anisotropy in the $\chi_3$ Anomaly in {URu$_2$Si$_2$}},
+ title = {Origin of the Large Anisotropy in the {$\chi_3$} Anomaly in {URu$_2$Si$_2$}},
  journal = {Journal of Physics: Conference Series},
  publisher = {IOP Publishing},
  year = {2013},
- month = {July},
+ month = {7},
  volume = {449},
  pages = {012026},
  url = {https://doi.org/10.1088%2F1742-6596%2F449%2F1%2F012026},
@@ -130,7 +130,7 @@ Ultrasound Spectroscopy and Machine Learning},
 @article{Cricchio_2009,
  author = {Cricchio, Francesco and Bultmark, Fredrik and Grånäs, Oscar and Nordström, Lars},
  title = {Itinerant Magnetic Multipole Moments of Rank Five as the Hidden Order in 
-URu$_2$Si$_2$},
+{URu$_2$Si$_2$}},
  journal = {Physical Review Letters},
  publisher = {American Physical Society (APS)},
  year = {2009},
@@ -144,7 +144,7 @@ URu$_2$Si$_2$},
 
 @article{deVisser_1986,
  author = {de Visser, A. and Kayzel, F. E. and Menovsky, A. A. and Franse, J. J. M. and van den Berg, J. and Nieuwenhuys, G. J.},
- title = {Thermal expansion and specific heat of monocrystalline URu$_2$Si$_2$},
+ title = {Thermal expansion and specific heat of monocrystalline {URu$_2$Si$_2$}},
  journal = {Physical Review B},
  publisher = {American Physical Society (APS)},
  year = {1986},
@@ -198,7 +198,7 @@ URu$_2$Si$_2$},
 
 @article{Guida_1998,
  author = {Guida, R. and Zinn-Justin, Jean},
- title = {Critical exponents of the $N$-vector model},
+ title = {Critical exponents of the {$N$}-vector model},
  journal = {Journal of Physics A: Mathematical and General},
  publisher = {IOP Publishing},
  year = {1998},
@@ -212,7 +212,7 @@ URu$_2$Si$_2$},
 
 @article{Harima_2010,
  author = {Harima, Hisatomo and Miyake, Kazumasa and Flouquet, Jacques},
- title = {Why the Hidden Order in URu$_2$Si$_2$ Is Still Hidden---One Simple Answer},
+ title = {Why the Hidden Order in {URu$_2$Si$_2$} Is Still Hidden---One Simple Answer},
  journal = {Journal of the Physical Society of Japan},
  publisher = {Physical Society of Japan},
  year = {2010},
@@ -226,7 +226,7 @@ URu$_2$Si$_2$},
 
 @article{Hassinger_2008,
  author = {Hassinger, E. and Knebel, G. and Izawa, K. and Lejay, P. and Salce, B. and Flouquet, J.},
- title = {Temperature-pressure phase diagram of URu$_\text2$Si$_\text2$ from resistivity measurements and ac calorimetry: Hidden order and Fermi-surface nesting},
+ title = {Temperature-pressure phase diagram of {URu$_2$Si$_2$} from resistivity measurements and ac calorimetry: Hidden order and {Fermi}-surface nesting},
  journal = {Physical Review B},
  publisher = {American Physical Society (APS)},
  year = {2008},
@@ -254,7 +254,7 @@ URu$_2$Si$_2$},
 
 @article{Haule_2009,
  author = {Haule, Kristjan and Kotliar, Gabriel},
- title = {Arrested Kondo effect and hidden order in URu$_\text2$Si$_\text2$},
+ title = {Arrested {Kondo} effect and hidden order in {URu$_2$Si$_2$}},
  journal = {Nature Physics},
  publisher = {Springer Science and Business Media LLC},
  year = {2009},
@@ -268,7 +268,7 @@ URu$_2$Si$_2$},
 
 @article{Hornreich_1980,
  author = {Hornreich, R. M.},
- title = {The Lifshitz point: Phase diagrams and critical behavior},
+ title = {The {Lifshitz} point: Phase diagrams and critical behavior},
  journal = {Journal of Magnetism and Magnetic Materials},
  publisher = {Elsevier BV},
  year = {1980},
@@ -279,13 +279,13 @@ URu$_2$Si$_2$},
  doi = {10.1016/0304-8853(80)91100-2}
 }
 
-@article{Hoshino_2013,
+@article{Hoshino_2013_Resolution,
  author = {Hoshino, Shintaro and Otsuki, Junya and Kuramoto, Yoshio},
- title = {Resolution of Entropy $łn\sqrt2$ by Ordering in Two-Channel Kondo Lattice},
+ title = {Resolution of Entropy {$\ln\sqrt2$} by Ordering in Two-Channel {Kondo} Lattice},
  journal = {Journal of the Physical Society of Japan},
  publisher = {Physical Society of Japan},
  year = {2013},
- month = {April},
+ month = {4},
  number = {4},
  volume = {82},
  pages = {044707},
@@ -293,13 +293,13 @@ URu$_2$Si$_2$},
  doi = {10.7566/jpsj.82.044707}
 }
 
-@article{Ikeda_1998,
+@article{Ikeda_1998_Theory,
  author = {Ikeda, Hiroaki and Ohashi, Yoji},
- title = {Theory of Unconventional Spin Density Wave: A Possible Mechanism of the Micromagnetism in U-based Heavy Fermion Compounds},
+ title = {Theory of Unconventional Spin Density Wave: A Possible Mechanism of the Micromagnetism in {U}-based Heavy Fermion Compounds},
  journal = {Physical Review Letters},
  publisher = {American Physical Society (APS)},
  year = {1998},
- month = {October},
+ month = {10},
  number = {17},
  volume = {81},
  pages = {3723--3726},
@@ -309,7 +309,7 @@ URu$_2$Si$_2$},
 
 @article{Ikeda_2012,
  author = {Ikeda, Hiroaki and Suzuki, Michi-To and Arita, Ryotaro and Takimoto, Tetsuya and Shibauchi, Takasada and Matsuda, Yuji},
- title = {Emergent rank-5 nematic order in URu$_\text2$Si$_\text2$},
+ title = {Emergent rank-5 nematic order in {URu$_2$Si$_2$}},
  journal = {Nature Physics},
  publisher = {Springer Science and Business Media LLC},
  year = {2012},
@@ -323,7 +323,7 @@ URu$_2$Si$_2$},
 
 @article{Inoue_2001,
  author = {Inoue, T. and Kindo, K. and Okuni, H. and Sugiyama, K. and Haga, Y. and Yamamoto, E. and Kobayashi, T. C. and Uwatoko, Y. and Onuki, Y.},
- title = {High-field magnetization of URu$_\text2$Si$_\text2$ under high pressure},
+ title = {High-field magnetization of {URu$_2$Si$_2$} under high pressure},
  journal = {Physica B: Condensed Matter},
  publisher = {Elsevier BV},
  year = {2001},
@@ -336,7 +336,7 @@ URu$_2$Si$_2$},
 
 @article{Kambe_2018,
  author = {Kambe, S. and Tokunaga, Y. and Sakai, H. and Hattori, T. and Higa, N. and Matsuda, T. D. and Haga, Y. and Walstedt, R. E. and Harima, H.},
- title = {Odd-parity electronic multipolar ordering in URu$_\text2$Si$_\text2$: Conclusions from Si and Ru NMR measurements},
+ title = {Odd-parity electronic multipolar ordering in {URu$_2$Si$_2$}: Conclusions from {Si} and {Ru} {NMR} measurements},
  journal = {Physical Review B},
  publisher = {American Physical Society (APS)},
  year = {2018},
@@ -350,7 +350,7 @@ URu$_2$Si$_2$},
 
 @article{Kiss_2005,
  author = {Kiss, Annamária and Fazekas, Patrik},
- title = {Group theory and octupolar order in URu$_\text2$Si$_\text2$},
+ title = {Group theory and octupolar order in {URu$_2$Si$_2$}},
  journal = {Physical Review B},
  publisher = {American Physical Society (APS)},
  year = {2005},
@@ -364,7 +364,7 @@ URu$_2$Si$_2$},
 
 @article{Kung_2015,
  author = {Kung, H.-H. and Baumbach, R. E. and Bauer, E. D. and Thorsmølle, V. K. and Zhang, W.-L. and Haule, K. and Mydosh, J. A. and Blumberg, G.},
- title = {Chirality density wave of the ``hidden order" phase in URu$_\text2$Si$_\text2$},
+ title = {Chirality density wave of the ``hidden order" phase in {URu$_2$Si$_2$}},
  journal = {Science},
  publisher = {American Association for the Advancement of Science (AAAS)},
  year = {2015},
@@ -376,9 +376,9 @@ URu$_2$Si$_2$},
  doi = {10.1126/science.1259729}
 }
 
-@article{Kusunose_2011,
+@article{Kusunose_2011_On,
  author = {Kusunose, Hiroaki and Harima, Hisatomo},
- title = {On the Hidden Order in URu$_\text2$Si$_\text2$---Antiferro Hexadecapole Order and Its Consequences},
+ title = {On the Hidden Order in {URu$_2$Si$_2$}---Antiferro Hexadecapole Order and Its Consequences},
  journal = {Journal of the Physical Society of Japan},
  publisher = {Physical Society of Japan},
  year = {2011},
@@ -392,7 +392,7 @@ URu$_2$Si$_2$},
 
 @article{Kuwahara_1997,
  author = {Kuwahara, Keitaro and Amitsuka, Hiroshi and Sakakibara, Toshiro and Suzuki, Osamu and Nakamura, Shintaro and Goto, Terutaka and Mihalik, Marián and Menovsky, Alois~A. and de~Visser, Anne and Franse, Jaap~J. ~M.},
- title = {Lattice Instability and Elastic Response in the Heavy Electron System URu$_\text2$Si$_\text2$},
+ title = {Lattice Instability and Elastic Response in the Heavy Electron System {URu$_2$Si$_2$}},
  journal = {Journal of the Physical Society of Japan},
  publisher = {Physical Society of Japan},
  year = {1997},
@@ -406,20 +406,22 @@ URu$_2$Si$_2$},
 
 @article{Lifshitz_1942a,
  author = {Lifshitz, Evgeniĭ Mikhaĭlovich},
- title = {On the theory of phase transitions of the second order {I.}~{Changes} of the elementary cell of a crystal in phase transitions of the second order},
+ title = {On the theory of phase transitions of the second order {I}},
  journal = {Proceedings of the USSR Academy of Sciences Journal of Physics},
  year = {1942},
  volume = {6},
- pages = {61}
+ pages = {61},
+ subtitle = {Changes of the elementary cell of a crystal in phase transitions of the second order}
 }
 
 @article{Lifshitz_1942b,
  author = {Lifshitz, Evgeniĭ Mikhaĭlovich},
- title = {On the theory of phase transitions of the second order {II.}~{Phase} transitions of the second order in alloys},
+ title = {On the theory of phase transitions of the second order {II}},
  journal = {Proceedings of the USSR Academy of Sciences Journal of Physics},
  year = {1942},
  volume = {6},
- pages = {251}
+ pages = {251},
+ subtitle = {Phase transitions of the second order in alloys}
 }
 
 @article{Luthi_1970,
@@ -438,7 +440,7 @@ URu$_2$Si$_2$},
 
 @article{Meng_2013,
  author = {Meng, Jian-Qiao and Oppeneer, Peter M. and Mydosh, John A. and Riseborough, Peter S. and Gofryk, Krzysztof and Joyce, John J. and Bauer, Eric D. and Li, Yinwan and Durakiewicz, Tomasz},
- title = {Imaging the Three-Dimensional Fermi-Surface Pairing near the Hidden-Order Transition in URu$_\text2$Si$_\text2$ Using Angle-Resolved Photoemission Spectroscopy},
+ title = {Imaging the Three-Dimensional {Fermi}-Surface Pairing near the Hidden-Order Transition in {URu$_2$Si$_2$} Using Angle-Resolved Photoemission Spectroscopy},
  journal = {Physical Review Letters},
  publisher = {American Physical Society (APS)},
  year = {2013},
@@ -452,8 +454,8 @@ URu$_2$Si$_2$},
 
 @article{Ohkawa_1999,
  author = {Ohkawa, Fusayoshi J and Shimizu, Hirofumi},
- title = {Quadrupole and dipole orders in URu$_\text2$Si$_\text2$},
- journal = {Journal of Physics: Condensed Matter},
+ title = {Quadrupole and dipole orders in {URu$_2$Si$_2$}},
+ journal = {Journal of Physics},
  publisher = {IOP Publishing},
  year = {1999},
  month = {November},
@@ -461,7 +463,8 @@ URu$_2$Si$_2$},
  volume = {11},
  pages = {L519--L524},
  url = {https://doi.org/10.1088%2F0953-8984%2F11%2F46%2F101},
- doi = {10.1088/0953-8984/11/46/101}
+ doi = {10.1088/0953-8984/11/46/101},
+ journalsubtitle = {Condensed Matter}
 }
 
 @article{Ramshaw_2015,
@@ -478,13 +481,13 @@ URu$_2$Si$_2$},
  doi = {10.1073/pnas.1421174112}
 }
 
-@article{Rau_2012,
+@article{Rau_2012_Hidden,
  author = {Rau, Jeffrey G. and Kee, Hae-Young},
  title = {Hidden and antiferromagnetic order as a rank-5 superspin in {URu$_2$Si$_2$}},
  journal = {Physical Review B},
  publisher = {American Physical Society (APS)},
  year = {2012},
- month = {June},
+ month = {6},
  number = {24},
  volume = {85},
  pages = {245112},
@@ -492,13 +495,13 @@ URu$_2$Si$_2$},
  doi = {10.1103/physrevb.85.245112}
 }
 
-@article{Riggs_2015,
+@article{Riggs_2015_Evidence,
  author = {Riggs, Scott C. and Shapiro, M. C. and Maharaj, Akash V and Raghu, S. and Bauer, E. D. and Baumbach, R. E. and Giraldo-Gallo, P. and Wartenbe, Mark and Fisher, I. R.},
- title = {Evidence for a nematic component to the hidden-order parameter in URu$_2$Si$_2$ from differential elastoresistance measurements},
+ title = {Evidence for a nematic component to the hidden-order parameter in {URu$_2$Si$_2$} from differential elastoresistance measurements},
  journal = {Nature Communications},
  publisher = {Springer Science and Business Media LLC},
  year = {2015},
- month = {March},
+ month = {3},
  number = {1},
  volume = {6},
  pages = {6425},
@@ -508,7 +511,7 @@ URu$_2$Si$_2$},
 
 @article{Santini_1994,
  author = {Santini, P. and Amoretti, G.},
- title = {Crystal Field Model of the Magnetic Properties of URu$_\text2$Si$_\text2$},
+ title = {Crystal Field Model of the Magnetic Properties of {URu$_2$Si$_2$}},
  journal = {Physical Review Letters},
  publisher = {American Physical Society (APS)},
  year = {1994},
@@ -522,7 +525,7 @@ URu$_2$Si$_2$},
 
 @article{Shekhter_2013,
  author = {Shekhter, Arkady and Ramshaw, B. J. and Liang, Ruixing and Hardy, W. N. and Bonn, D. A. and Balakirev, Fedor F. and McDonald, Ross D. and Betts, Jon B. and Riggs, Scott C. and Migliori, Albert},
- title = {Bounding the pseudogap with a line of phase transitions in YBa$_\text2$Cu$_\text3$O$_\text6+δ$},
+ title = {Bounding the pseudogap with a line of phase transitions in {YBa$_2$Cu$_3$O$_{6+\delta}$}},
  journal = {Nature},
  publisher = {Springer Science and Business Media LLC},
  year = {2013},
@@ -536,7 +539,7 @@ URu$_2$Si$_2$},
 
 @article{Thalmeier_2011,
  author = {Thalmeier, Peter and Takimoto, Tetsuya},
- title = {Signatures of hidden-order symmetry in torque oscillations, elastic constant anomalies, and field-induced moments in URu$_\text2$Si$_\text2$},
+ title = {Signatures of hidden-order symmetry in torque oscillations, elastic constant anomalies, and field-induced moments in {URu$_2$Si$_2$}},
  journal = {Physical Review B},
  publisher = {American Physical Society (APS)},
  year = {2011},
@@ -548,13 +551,13 @@ URu$_2$Si$_2$},
  doi = {10.1103/physrevb.83.165110}
 }
 
-@article{Tonegawa_2012,
+@article{Tonegawa_2012_Cyclotron,
  author = {Tonegawa, S. and Hashimoto, K. and Ikada, K. and Lin, Y. -H. and Shishido, H. and Haga, Y. and Matsuda, T. D. and Yamamoto, E. and Onuki, Y. and Ikeda, H. and Matsuda, Y. and Shibauchi, T.},
- title = {Cyclotron Resonance in the Hidden-Order Phase of URu$_\text2$Si$_\text2$},
+ title = {Cyclotron Resonance in the Hidden-Order Phase of {URu$_2$Si$_2$}},
  journal = {Physical Review Letters},
  publisher = {American Physical Society (APS)},
  year = {2012},
- month = {July},
+ month = {7},
  number = {3},
  volume = {109},
  pages = {036401},
@@ -577,8 +580,8 @@ URu$_2$Si$_2$},
 }
 
 @article{Wiebe_2007,
- author = {Wiebe, C. R. and Janik, J. A. and MacDougall, G. J. and Luke, G. M. and Garrett, J. D. and Zhou, H. D. and Jo, Y. -J. and Balicas, L. and Qiu, Y. and Copley, J. R. D. and Yamani, Z. and Buyers, W. J. L.},
- title = {Gapped itinerant spin excitations account for missing entropy in the hidden-order state of URu$_\text2$Si$_\text2$},
+ author = {Wiebe, C. R. and Janik, J. A. and MacDougall, G. J. and Luke, G. M. and Garrett, J. D. and Zhou, H. D. and Jo, Y.-J. and Balicas, L. and Qiu, Y. and Copley, J. R. D. and Yamani, Z. and Buyers, W. J. L.},
+ title = {Gapped itinerant spin excitations account for missing entropy in the hidden-order state of {URu$_2$Si$_2$}},
  journal = {Nature Physics},
  publisher = {Springer Science and Business Media LLC},
  year = {2007},
@@ -592,7 +595,7 @@ URu$_2$Si$_2$},
 
 @article{Wolf_1994,
  author = {Wolf, B. and Sixl, W. and Graf, R. and Finsterbusch, D. and Bruls, G. and Lüthi, B. and Knetsch, E. A. and Menovsky, A. A. and Mydosh, J. A.},
- title = {Elastic properties of the heavy fermion superconductor URu$_\text2$Si$_\text2$},
+ title = {Elastic properties of the heavy fermion superconductor {URu$_2$Si$_2$}},
  journal = {Journal of Low Temperature Physics},
  publisher = {Springer Science and Business Media LLC},
  year = {1994},