DONE

1 files changed, 26 insertions, 20 deletions

diff --git a/aps_mm_2018.html b/aps_mm_2018.html
index 3be9597..a12c96e 100644
--- a/aps_mm_2018.html
+++ b/aps_mm_2018.html
@@ -92,7 +92,7 @@ Correlation time `\(\tau\sim L^z\)` at critical point, `\(\tau\sim t^{-z/\nu}\)`
   ]
 
   .column[
-<video width="320" height="320"><source src="figs/metropolis_ising_zerofield.webm" type="video/webm"></video>
+<video width="320" height="320" style="float: right;"><source src="figs/metropolis_ising_zerofield.webm" type="video/webm"></video>
 ]
 
 ---
@@ -119,7 +119,7 @@ Fast near the critical point: early studies thought `\(z\)` was zero for 2D Isin
   ]
 
   .column[
-<video width="320" height="320"><source src="figs/wolff_ising_zerofield.webm" type="video/webm"></video>
+<video width="320" height="320" style="float: right;"><source src="figs/wolff_ising_zerofield.webm" type="video/webm"></video>
 ]
 
 ---
@@ -138,7 +138,7 @@ class: split-40
 
 # Applying an *arbitrary* field
 
-  Introduce an extra &ldquo;spin&rdquo; `\(r_0\in R\)` whose possible configurations come from the set of *rotations*, not the set of spin states.
+  Introduce an extra &ldquo;spin&rdquo; `\(s_0\in R\)` whose possible configurations come from the set of *rotations*, not the set of spin states.
 
   Mark this spin a neighbor of every spin on the lattice.
 
@@ -147,8 +147,8 @@ class: split-40
     \tilde Z(s,t)=
     \begin{cases}
       Z(s,t) & \text{if $s,t\in X$}\\
-      H(t^{-1}\cdot s) & \text{if $t\in R$}\\
-      H(s^{-1}\cdot t) & \text{if $s\in R$}
+      B(t^{-1}\cdot s) & \text{if $t\in R$}\\
+      B(s^{-1}\cdot t) & \text{if $s\in R$}
     \end{cases}
   \]`
 
@@ -156,11 +156,11 @@ class: split-40
 
   Exact correspondence between expectation values of operators in old and new
   models: if `\(A(\{s\})\)` is an observable on old model in field, `\(\tilde
-  A(r_0,\{s\})=A(\{r_0^{-1}\cdot s\})\)` has the property
+  A(s_0,\{s\})=A(\{s_0^{-1}\cdot s\})\)` has the property
   `\[
     \langle\tilde
-    A\rangle=\mathop{\mathrm{Tr}}\nolimits_{r_0\in R}\mathop{\mathrm{Tr}}\nolimits_{\{s\}\in X^N}\tilde
-    A(r_0,\{s\})=\mathop{\mathrm{Tr}}\nolimits_{\{s\}\in X^N}A(\{s\})=\langle A\rangle
+    A\rangle=\mathop{\mathrm{Tr}}\nolimits_{s_0\in R}\mathop{\mathrm{Tr}}\nolimits_{\{s\}\in X^N}\tilde
+    A(s_0,\{s\})=\mathop{\mathrm{Tr}}\nolimits_{\{s\}\in X^N}A(\{s\})=\langle A\rangle
   \]`
 
   ]
@@ -175,7 +175,7 @@ class: split-40
 
 <img src="figs/vector-1.svg" alt="order-n" style="float: left;"/>
 <img src="figs/vector-2.svg" alt="order-n" style="float: right;"/>
-<span style="font-size: 30pt; overflow: hidden; height: 7em; text-align: center; align-items: center; display: inline-flex; position: static; float: center">&nbsp;&nbsp;`\[\xrightarrow{r\in O(2)}\]`</span>
+<span style="font-size: 30pt; overflow: hidden; height: 7em; text-align: center; align-items: center; display: inline-flex; position: static; float: center">&nbsp;&nbsp;`\[\xrightarrow{r\in \mathrm O(2)}\]`</span>
 
 ---
 
@@ -213,6 +213,8 @@ class: split-40
 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).
+
+Near-constant runtime as field is varied at high, low temperature, strictly faster than zero field at critical point.
 ]
 
 .column[
@@ -223,7 +225,7 @@ Pictured: 2D Ising (`\(128\times128\)`) correlation time as a function of field
 
 # Correlation time scaling
 
-Correlation time scales consistently in the whole phase space!
+Correlation time scales consistently in the whole phase space: a natural extension of the algorithm's dynamics!
 
 Pictured: scaling collapses of 2D Ising model correlation time.
 
@@ -233,31 +235,35 @@ Pictured: scaling collapses of 2D Ising model correlation time.
 ---
 class: split-50
 # Applications &amp; future work
-.column[ #### Direct measurements in metastable states
-
-Rapid sampling of states near the critical point of models in a small field occasionally yields microstates against the direction of the field.
-
-<img src="figs/metastable-scaling.png" style="width: 80%; float: left;" />
-]
-
 .column[
 
 #### Symmetry-breaking perturbations of XY model
 
-For various values of `\(p\)`, external fields of the form
+For various integer values `\(p\)`, external fields of the form
 
 `\[
-H_p(s)=\cos(p\theta(s))
+B_p(s)=H\cos(p\theta(s))
 \]`
 
 have various effects on the criticality of the XY model.
+
+Theory from Joeé, Kadanoff, Kirkpatrick, & Nelson: perturbations are relevant *except* for `\(p=6\)`.
+
+We can test it!
+]
+
+.column[ #### Direct measurements in metastable states
+
+Rapid sampling of states near the critical point of models in a small field occasionally yields microstates against the direction of the field.
+
+<img src="figs/metastable-scaling.png" style="width: 47%;" />
 ]
 
 ---
 
 # Questions?
 
-<video><source src="figs/wolff_xy_field.webm" type="video/webm"></video>
+<video style="margin-left: auto; margin-right: auto; margin: 0 auto; display: block; width: 75%;"><source src="figs/wolff_xy_field.webm" type="video/webm"></video>
 
    </textarea>
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