From cffd9d74d071532fd7a43105e7c01f03d5ccea95 Mon Sep 17 00:00:00 2001 From: Alex Schmidt Date: Wed, 6 Nov 2013 12:16:50 +0100 Subject: [PATCH] Ydalia: I corrected some small things (in the text and my figures) and added one reference to [2]. --- .gitignore | 1 + pics/aphi-eps-converted-to.pdf | Bin 11851 -> 0 bytes pics/aphi.eps | 672 ++++------ pics/bn-eps-converted-to.pdf | Bin 11895 -> 0 bytes pics/bn.eps | 1778 +++++++++++++------------- pics/f-eps-converted-to.pdf | Bin 10376 -> 0 bytes pics/plaquettes-eps-converted-to.pdf | Bin 5476 -> 0 bytes pics/segments-eps-converted-to.pdf | Bin 5465 -> 0 bytes pics/segments.pdf | Bin 5434 -> 5550 bytes pics/u2-eps-converted-to.pdf | Bin 8674 -> 0 bytes pics/u2.eps | 142 +- pics/worm-eps-converted-to.pdf | Bin 6768 -> 0 bytes proceed.tex | 31 +- test | 0 14 files changed, 1236 insertions(+), 1388 deletions(-) delete mode 100644 pics/aphi-eps-converted-to.pdf delete mode 100644 pics/bn-eps-converted-to.pdf delete mode 100644 pics/f-eps-converted-to.pdf delete mode 100644 pics/plaquettes-eps-converted-to.pdf delete mode 100644 pics/segments-eps-converted-to.pdf delete mode 100644 pics/u2-eps-converted-to.pdf delete mode 100644 pics/worm-eps-converted-to.pdf delete mode 100644 test diff --git a/.gitignore b/.gitignore index f2c6592..395f4d2 100644 --- a/.gitignore +++ b/.gitignore @@ -3,3 +3,4 @@ *.log *~ proceed.pdf +pics/*-converted-to.pdf diff --git a/pics/aphi-eps-converted-to.pdf b/pics/aphi-eps-converted-to.pdf deleted file mode 100644 index a25ff95f46f66370cd565ab837fef699138eb524..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 11851 zcmb_?2{@G9`!KQ&*=3EfWj71Pk|j%a+4m)b8OAch7#Ul3AtaHdNS4SFl{KqfpeYRsH% zt`;8Ly@p%P`lPY9;J3xt*ZRDmv-XvMY2Win0qjym&&w(se!cu9^d@Y4?DLwASY-(R zrqi~{$T0OH(Y&{Uq3Qzf;^>>Y~+qE zJ$&b0b$)3f>68ssn@U~Yd+|k`%JUDZveMLxtos-3+#A1gy`TR=EV?`9Ygc^v4J`0F zUvPZ2;X@v(%5jx9O^y+XL2Kcv!;dSpg;jg*kKs!+U%fktJR<+9%`snWJoN4X`K7Ta 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z?$ce&#>$qjpAWHVuNG_zwMuHV2&%^HOvxQ^lF=zy*L5i5(hj9E8Y8V_{R6YRVV58{i{#! zXsMa*zqZS3Fpaq^PHE25j)tuFDQw!oRhN9u1o!KVUL6_fW?$CkjHOclYPf2w-OCxu zX?^++=i%=a^F(d^Gt>2Qu>YCn5(q!e2orN5$gM*e0%RZ~m=$iS)n8Gmg=Eo9wLI|- zC6Po`Q-fq-iSLDA9C2GLjp4lfu&lSm{8R8ts? zKA_O&$Ak;0Lj7>Q8kkQk2+QjSTR7i9ERz9^!-iO15ZV9*O-wXVSg|AWe86fYF6I6k)=89;SUEg5;1Xsl zc%bsr#~YvxFqrQ%iOI*YCJ=0!Nm}{0^+e@5IQ;LLVzXgahUtu~IkZSNsFUri|38lM zZ`+nm`yntlk{2f46?7WJ2xGvq@qu~KKw>)0D2T&jQ-M!Yxm-}sQw6})A>fNzW+nhB zUgU7>I)pUDCJhZs5?q&Wi6 zHDf^Rm~f7O!H2k@J;?w~&G2A;0H4aEhA^Ty0kBI!To#QFMPdx7!QkB{Y|Sv1+4mdq zywFcsz#R>CDh}_vIIfI{3AxO`oWF64u`u@!o`3KaF$kO~z-^!(Czcrk`7eF`y@7rn z(;yi()ry7>;Xl%1xT!au6;GTe+W&N%=zydYRwOVuyg#+AjbKZF9uyW$z>&oJS__5J z0%TzS{~r|NyHR`cJ_U?!u={BLTaEz+w1^ZiIXrD(XPqDIUm=eX1bTO9A_6{szklFv z78Z{TLXN{QI1K0w!5?J!1k8{G_W^%}VXy>{Z~q3vz}Bv2>Nxu z@`5JmAM;`{M9`1?jgAC&ihqUSQAA+gUtt(L_D^0s;SU%VZ}^8Scr08*{W=~nKS(5g zg%PlmWfAbGpx?#=|3iU) show GR /Font9 FFSF -0.1773 0.4104 m +0.1920 0.4127 m GS -[0.0184 0.0000 0.0000 0.0184 0 0] CC +[0.0170 0.0000 0.0000 0.0170 0 0] CC (SWA) show GR /Font9 FFSF -0.2425 0.4114 m +0.2466 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (<|) show GR /Symbol findfont /Font30 exch definefont pop /Font30 FFSF -0.2645 0.4114 m +0.2670 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (f) show GR /Font9 FFSF -0.2782 0.4114 m +0.2795 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (|) show GR /Font9 FFSF -0.2852 0.4271 m +0.2858 0.4278 m GS -[0.0184 0.0000 0.0000 0.0184 0 0] CC +[0.0170 0.0000 0.0000 0.0170 0 0] CC (2) show GR /Font9 FFSF -0.2954 0.4114 m +0.2952 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (>) show GR /Font9 FFSF -0.3107 0.4010 m +0.3094 0.4038 m GS -[0.0184 0.0000 0.0000 0.0184 0 0] CC +[0.0170 0.0000 0.0000 0.0170 0 0] CC (SWA) show GR /Font9 FFSF [/DeviceRGB] SCS Color1 SC -0.3779 0.4208 m +0.3659 0.4224 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC -(U) show +[0.0241 0.0000 0.0000 0.0241 0 0] CC +() show GR /Font9 FFSF -0.3967 0.4104 m +0.4114 0.4127 m GS -[0.0184 0.0000 0.0000 0.0184 0 0] CC +[0.0170 0.0000 0.0000 0.0170 0 0] CC (LMA) show GR /Font9 FFSF -0.4618 0.4114 m +0.4660 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (<|) show GR /Font30 FFSF -0.4838 0.4114 m +0.4864 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (f) show GR /Font9 FFSF -0.4975 0.4114 m +0.4989 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (|) show GR /Font9 FFSF -0.5046 0.4271 m +0.5052 0.4278 m GS -[0.0184 0.0000 0.0000 0.0184 0 0] CC +[0.0170 0.0000 0.0000 0.0170 0 0] CC (2) show GR /Font9 FFSF -0.5148 0.4114 m +0.5146 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (>) show GR /Font9 FFSF -0.5301 0.4010 m +0.5287 0.4038 m GS -[0.0184 0.0000 0.0000 0.0184 0 0] CC +[0.0170 0.0000 0.0000 0.0170 0 0] CC (LMA) show GR n @@ -1138,101 +1138,101 @@ s /Font9 FFSF [/DeviceRGB] SCS Color2 SC -0.6785 0.4208 m +0.6665 0.4224 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC -(U) show +[0.0241 0.0000 0.0000 0.0241 0 0] CC +() show GR /Font9 FFSF -0.6973 0.4104 m +0.7120 0.4127 m GS -[0.0184 0.0000 0.0000 0.0184 0 0] CC +[0.0170 0.0000 0.0000 0.0170 0 0] CC (SWA) show GR /Font9 FFSF -0.7625 0.4114 m +0.7666 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (<|) show GR /Font30 FFSF -0.7845 0.4114 m +0.7870 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (f) show GR /Font9 FFSF -0.7982 0.4114 m +0.7995 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (|) show GR /Font9 FFSF -0.8052 0.4271 m +0.8058 0.4278 m GS -[0.0184 0.0000 0.0000 0.0184 0 0] CC +[0.0170 0.0000 0.0000 0.0170 0 0] CC (2) show GR /Font9 FFSF -0.8154 0.4114 m +0.8152 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (>) show GR /Font9 FFSF -0.8307 0.4010 m +0.8294 0.4038 m GS -[0.0184 0.0000 0.0000 0.0184 0 0] CC +[0.0170 0.0000 0.0000 0.0170 0 0] CC (SWA) show GR /Font9 FFSF [/DeviceRGB] SCS Color1 SC -0.8979 0.4208 m +0.8859 0.4224 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC -(U) show +[0.0241 0.0000 0.0000 0.0241 0 0] CC +() show GR /Font9 FFSF -0.9167 0.4104 m +0.9314 0.4127 m GS -[0.0184 0.0000 0.0000 0.0184 0 0] CC +[0.0170 0.0000 0.0000 0.0170 0 0] CC (LMA) show GR /Font9 FFSF -0.9818 0.4114 m +0.9860 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (<|) show GR /Font30 FFSF -1.0038 0.4114 m +1.0064 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (f) show GR /Font9 FFSF -1.0175 0.4114 m +1.0189 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (|) show GR /Font9 FFSF -1.0246 0.4271 m +1.0252 0.4278 m GS -[0.0184 0.0000 0.0000 0.0184 0 0] CC +[0.0170 0.0000 0.0000 0.0170 0 0] CC (2) show GR /Font9 FFSF -1.0348 0.4114 m +1.0346 0.4134 m GS -[0.0260 0.0000 0.0000 0.0260 0 0] CC +[0.0241 0.0000 0.0000 0.0241 0 0] CC (>) show GR /Font9 FFSF -1.0501 0.4010 m +1.0487 0.4038 m GS -[0.0184 0.0000 0.0000 0.0184 0 0] CC +[0.0170 0.0000 0.0000 0.0170 0 0] CC (LMA) show GR n @@ -1578,7 +1578,7 @@ GS ( = 1.1) show GR %%Trailer -%%BoundingBox: 16 244 706 522 +%%BoundingBox: 16 245 706 522 %%DocumentNeededResources: font Helvetica %%+ font Symbol %%EOF diff --git a/pics/worm-eps-converted-to.pdf b/pics/worm-eps-converted-to.pdf deleted file mode 100644 index 6421ce7800da2f1aef4a66f2e228c1daf62a777a..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 6768 zcmb_h30xCb(63sp#tUuLq9BV(!xc8Wxg&?1f*3$RKsjVd76^nSCL0b9P?RcC6|vv} z0!pP?tw&W*P*Dykh@utIs(@Dos)7nFiYVXP$Pthp-}g270lV{N=FOX#|Gaq*12;Pd z8e+zz7?eNTx{tzw=#VTZjACvMFT|xGL@2}t6nEG`EFo|O1UpDD0=L73G7)ZRNl_9C 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The dual variables are link- and plaquette occupation numbers, subject to local constraints that have to be respected by the Monte Carlo algorithm. For the simulation we use a local update as well as the newly developed -''surface worm algorithm'', which is a generalization of the Prokof'ev Svistunov +``surface worm algorithm'', which is a generalization of the Prokof'ev Svistunov worm algorithm concept for simulating the dual representation of abelian Gauge-Higgs models on a lattice. We assess the performance of the two algorithms, present results for the phase diagram @@ -226,9 +226,9 @@ raising or lowering their occupation number by one unit. \item ``Plaquette update'': It consists of increasing or decreasing a plaquette occupation number $p_{x,\nu\rho}$ and -the link fluxes (either $l_{x,\sigma}$ or $j_{x,\sigma}$) at the edges of $p_{x,\nu\rho}$ by $\pm 1$ as +the link fluxes (either $j_{x,\sigma}$ or $l_{x,\sigma}$) at the edges of $p_{x,\nu\rho}$ by $\pm 1$ as illustrated in Fig.~\ref{plaquette}. The change of $p_{x, \nu \rho}$ -by $\pm 1$ is indicated by the signs $+$ or $-$, while the flux variables $l$ ($j$) are denoted by the thin red line +by $\pm 1$ is indicated by the signs $+$ or $-$, while the flux variables $j$ ($l$) are denoted by the thin red line (fat blue lines for the second flavor) and we use a dashed line to indicate a decrease by $-1$ and a full line for an increase by $+1$. % @@ -240,7 +240,7 @@ in time direction are the only objects that couple to the chemical potential. % \vspace*{-1mm} \item ``Cube update'': The plaquettes of 3-cubes -of our 4d lattice are changed according to one of the two patterns illustrated in +of our 4-d lattice are changed according to one of the two patterns illustrated in Fig.~\ref{cube}. Although the plaquette and winding loop update are enough to satisfy ergodicity, the cube update helps for decorrelation in the region of @@ -258,7 +258,7 @@ probability computed from the local weight factors. \end{center} \vspace{-4mm} \caption{Plaquette update: A plaquette occupation number is changed by $+1$ or -$-1$ and the links $l$ (thin red links) or $j$ (fat blue links) of the plaquette are changed simultaneously. The +$-1$ and the links $j$ (thin red links) or $l$ (fat blue links) of the plaquette are changed simultaneously. The full line indicates an increase by +1 and a dashed line a decrease by $-1$. The directions $1 \le \nu_1 < \nu_2 \le 4$ indicate the plane of the plaquette.} \label{plaquette} @@ -290,11 +290,11 @@ The admissible configurations are generated using 3 elements: \begin{enumerate} \item The worm starts by changing either the $l$ or the $j$ flux by $\pm 1$ at -a randomly chosen link (step 1 in Fig.~\ref{worm} where a worm for $l$ fluxes starts). +a randomly chosen link (step 1 in Fig.~\ref{worm} where a worm for $j$ fluxes starts). \item The first link becomes the head of the worm $L_V$. The defect at $L_V$ is then propagated through the lattice by -attaching segments of the same kind of flux ($l$ or $j$) as the first segment, +attaching segments of the same kind of flux ($j$ or $l$) as the first segment, which are chosen in such a way that the constraints are always obeyed at the link where the next segment is attached (step 2 in Fig.~\ref{worm}). @@ -312,7 +312,7 @@ and a sweep of winding loops (as explained for the LMA). \includegraphics[width=\textwidth,clip]{pics/segments} \end{center} \vspace{-4mm} -\caption{Examples of segments for the links $l$ (lhs.) and $j$ (rhs.) +\caption{Examples of segments for the links $j$ (lhs.) and $l$ (rhs.) in the $\nu_1$-$\nu_2$-plane ($\nu_1 < \nu_2$). The plaquette occupation numbers are changed as indicated by the signs. The full (dashed) links are changed by $+1$ ($-1$). The empty link shows @@ -357,7 +357,7 @@ and its susceptibility which are the first and second derivatives with respect to the chemical potential, \begin{equation} -n = \frac{1}{N_s^3 N_t}\frac{\partial}{\partial \mu} \ln\ Z\quad , \quad +\langle n \rangle = \frac{1}{N_s^3 N_t}\frac{\partial}{\partial \mu} \ln\ Z\quad , \quad \chi_{n} = \frac{1}{N_s^3 N_t}\frac{\partial^2}{\partial \mu^2} \ln\ Z\ . \end{equation} @@ -382,10 +382,10 @@ $\langle |\phi|^2 \rangle$ (lhs.) and the corresponding susceptibility (rhs.) as $\mu_\phi = \mu_\chi = \mu$ at $\beta = 0.85$ and $M_\phi^2 = M_\chi^2 = M^2 = 5.325$ on a lattice of size $12^3 \times 60$. This point is located in the Higgs phase and does not show any phase transition as a function of $\mu$. The bottom -plots show the particle number $n$ (lhs.) and its susceptibility (rhs.) as a function of $\mu$ +plots show the particle number $\langle n \rangle$ (lhs.) and its susceptibility (rhs.) as a function of $\mu$ for $\beta = 0.75$ and $M^2 = 5.73$ on a lattice of volume $12^3 \times 60$. Here we observe a pronounced first order transition from the confining phase into the Higgs phase. -It is obvious that in all four plots the agreement between the results from the LWA and from the +It is obvious that in all four plots the agreement between the results from the LMA and from the SWA is excellent. \begin{figure}[h] @@ -411,7 +411,7 @@ On the other hand, for parameter values where the constrained links have a very the worm algorithm has difficulties to efficiently sample the system because it changes the link occupation number in every move, while the LMA has a sweep with only closed surfaces. The plot on the rhs. of Fig.~\ref{auto} shows how $\overline{\tau}$ for -$U$ is larger for the SWA than for the LMA. We remark however, that this performance issue +$\langle U \rangle$ is larger for the SWA than for the LMA. We remark however, that this performance issue can be overcome easily by augmenting the SWA with sweeps of cube updates as used in the LMA. \begin{figure}[t] @@ -617,6 +617,13 @@ and by the Austrian Science Fund FWF Grant.\ Nr.\ I 1452-N27. %``The silver blaze property for QCD with heavy quarks from the lattice,'' Phys.\ Rev.\ Lett. 110 (2013) 122001. %%CITATION = ARXIV:1207.3005;%% +% + K.~Langfeld, B.~Lucini and A.~Rago, + %``The density of states in gauge theories,'' + Phys.\ Rev.\ Lett.\ {\bf 109} (2012) 111601 + [arXiv:1204.3243 [hep-lat]]. + %%CITATION = ARXIV:1204.3243;%% + %4 citations counted in INSPIRE as of 05 Nov 2013 \bibitem{dual} diff --git a/test b/test deleted file mode 100644 index e69de29..0000000 -- 2.39.5