From bb10258c700c70936eb1918b57e89a913bb3476e Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Thu, 8 Mar 2018 18:25:06 -0500 Subject: new figures --- aps_mm_2018.html | 33 +++++++++++++++++++++++++-------- figs/wolff_potts_field.webm | Bin 1039359 -> 1020371 bytes figs/wolff_potts_field_2.webm | Bin 2562438 -> 0 bytes time_compare.png | Bin 0 -> 18422 bytes 4 files changed, 25 insertions(+), 8 deletions(-) delete mode 100644 figs/wolff_potts_field_2.webm create mode 100644 time_compare.png diff --git a/aps_mm_2018.html b/aps_mm_2018.html index a3f6d91..3be9597 100644 --- a/aps_mm_2018.html +++ b/aps_mm_2018.html @@ -39,14 +39,14 @@ class: center, middle Described by Hamiltonians whose degrees of freedom are spins `\(s\in X\)` -$$\mathcal H=-\sum_{\langle ij\rangle}Z(s_i,s_j)-\sum_iH(s_i)$$ +$$\mathcal H=-\sum_{\langle ij\rangle}Z(s_i,s_j)-\sum_iB(s_i)$$ for \\(Z\\) invariant under the action of rotations \\(r\in R\\), or \\(Z(r\cdot s,r\cdot t)=Z(s,t)\\). - + @@ -54,13 +54,13 @@ for \\(Z\\) invariant under the action of rotations \\(r\in R\\), or \\(Z(r\cdot - + - + - +
XRGroup Action\(Z(s,t)\)\(H(s)\)XRGroup Action\(Z(s,t)\)\(B(s)\)
Ising model\(\{-1,1\}\)ℤ/2ℤ\(0\cdot s\mapsto s\)
\(1\cdot s\mapsto-s\)		\(s\times t\)\(Hs\)
Order-\(n\) model\(S^n\)\(\mathop{\mathrm{O}}(n)\)\(O\cdot s\mapsto Os\)\(s^{\mathrm T}t\)\(H\cdot s\)Order-\(n\) model\(S^n\)\(\mathop{\mathrm{O}}(n)\)\(O\cdot s\mapsto Os\)\(s^{\mathrm T}t\)\(H^{\mathrm T}s\)
Potts modelℤ/qℤℤ/qℤ\(m\cdot s\mapsto{(s+m)}\pmod q\)\(\delta(s,t)\)\(\sum_mH_m\delta(m,s)\)Potts model{0,…,q – 1}DqRotation & reflection
of polygon vertices		\(\delta(s,t)\)\(\sum_mH_m\delta(m,s)\)
Clock modelℤ/qℤℤ/qℤ\(m\cdot s\mapsto{(s+m)}\pmod q\)\(\cos(2\pi\frac{s-t}q)\)\(\sum_mH_m\cos(2\pi\frac{s-m}q)\)Clock model{0,…,q – 1}DqRotation & reflection
of polygon vertices		\(\cos(2\pi\frac{s-t}q)\)\(\sum_mH_m\cos(2\pi\frac{s-m}q)\)
@@ -188,9 +188,9 @@ class: split-40 Consider the clock Potts model with field `\[ H(m)=0.01\times\begin{cases} -0 & \text{if $m=0$ (black)}\\ -\cos(2\pi/6) & \text{if $m=1$ (grey}\\ --\cos(2\pi/6) & \text{if $m=2$ (white)} +0 & \text{if $m=0$ (blue)}\\ +\cos(2\pi/6) & \text{if $m=1$ (green}\\ +-\cos(2\pi/6) & \text{if $m=2$ (yellow)} \end{cases} \]` @@ -204,6 +204,23 @@ No rotation `\(r\in\mathbb Z/3\mathbb Z\)` that takes field to the identity! --- +class: split-40 + +.column[ + +# Correlation time comparison + +The correlation time of this algorithm beats metropolis and hybrid Wolff/metropolis in whole phase space! + +Pictured: 2D Ising (`\(128\times128\)`) correlation time as a function of field for three algorithms in high-temperature phase (top), at `\(T_c\)` (middle), and in the low temperature phase (bottom). +] + +.column[ + +] + +--- + # Correlation time scaling Correlation time scales consistently in the whole phase space! diff --git a/figs/wolff_potts_field.webm b/figs/wolff_potts_field.webm index b97c976..2d0d230 100644 Binary files a/figs/wolff_potts_field.webm and b/figs/wolff_potts_field.webm differ diff --git a/figs/wolff_potts_field_2.webm b/figs/wolff_potts_field_2.webm deleted file mode 100644 index 2aa4c8d..0000000 Binary files a/figs/wolff_potts_field_2.webm and /dev/null differ diff --git a/time_compare.png b/time_compare.png new file mode 100644 index 0000000..035531a Binary files /dev/null and b/time_compare.png differ -- cgit v1.2.3-70-g09d2