-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathplotTransitionPtsHigherAccuracySmallLzz.m
173 lines (152 loc) · 6.47 KB
/
plotTransitionPtsHigherAccuracySmallLzz.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
aaa = readmatrix('tranptsHigherAccuracyl=1lz=0p005.txt');
lnz=1;
lzz=0.005;
kappazero = sqrt(lzz/(1+lzz));
slopezero =pi^2/4 *(1/lzz-1)/(1/sqrt(lzz)+sqrt(lzz));
betajbegin=1/aaa(1,1);
betajend = 1/aaa(end,1);
kappaend = aaa(end, 2);
datasplitpoint =10; %only low temperature point obey linear relation
aaalinear =aaa(1:datasplitpoint,:);
aaaremain = aaa(datasplitpoint+1:end,:);
%inter= @(x) interp1(aaa(:,1),aaa(:,2),x,'spline','extrap');
% template = hgload('phasediagramloglog.fig');
% ax=gca;
% ha1 = findobj(template,'Type','Legend');
%
%
% [p,S, mu]=polyfit(aaalinear(:,1),aaalinear(:,2),1);
[p,S]=polyfit(aaalinear(:,1),aaalinear(:,2),1);
pltx2 = linspace(0,1.5*aaalinear(end,1),100);
% [y,delta] = polyval(p,pltx2,S,mu);
% plot(pltx2,y+2*delta,'m--',pltx2,y-2*delta,'m--')
% hold on
% plot(aaalinear(:,1),aaalinear(:,2),"o","MarkerSize",4)
%%
ff = figure;
subplot(1,2,1)
pltx = linspace(0,1/betajend,100);
%plotdat = inter(pltx);
%plotdat = exp(p(2))* pltx.^(p(1));
%plot(pltx,plotdat, aaalinear(:,1),aaalinear(:,2),"o","MarkerSize",4)
plot(aaa(1:end-1,1),aaa(1:end-1,2),"-o",'Color','Red',"MarkerSize",4)
% hold on
% plot(aaaremain(:,1),aaaremain(:,2),"-*","MarkerSize",4)
hold on
plot(1/betajend,kappaend,"*","Color","black","MarkerSize",4)
hold on
plot(aaa(end-1:end,1),aaa(end-1:end,2),"-",'Color','Red',"MarkerSize",4)
set(gca,'FontSize',16)
secondorderPtstring = append( '(', num2str(1/betajend,'%.3g'), ',', num2str(kappaend,'%.3g'), ')');
text(1/betajend-0.004,kappaend-0.03,secondorderPtstring,'FontSize', 11)
text(0.5/betajend -0.03,0.5*kappaend+0.25,'polarized phase','FontSize', 16)
text(0.5/betajend,0.5*kappaend,'chaotic phase','FontSize', 16)
xlim([0 1.2/betajend])
ylim([0 kappaend*1.5])
%titlestr2 = 'Phase diagram, linear scale';
titlestr2 = append('Phase diagram ($l_{nz}$ =', num2str(lnz,'%.4g'), ', $l_{zz}$ = ', num2str(lzz,'%.4g'),')');
title(titlestr2,'Interpreter','latex')
xlabel('$1/(\beta \mathbf{J})$','Interpreter','latex')
ylabel('$\kappa$','Interpreter','latex')
% legstr21 = append('$\kappa =', num2str( exp(p(2)),'%.4f'),'(1/\beta \mathbf{J})^{', num2str(p(1),'%.4f'),'}$');
legstr22 = 'first-order transition points';
% legstr23 = 'other first-order transition points';
legstr24 = 'second-order transition point'
legend(legstr22,legstr24,'Interpreter','latex','Location', 'southeast','FontSize', 16)
grid on
subplot(1,2,2)
plot(pltx2, p(1)*pltx2+ p(2),'-','Color','Blue');
hold on
plot(aaalinear(:,1),aaalinear(:,2),"o",'Color','Red',"MarkerSize",4)
hold on
plot(aaaremain(:,1),aaaremain(:,2),"o","MarkerSize",4)
set(gca,'FontSize',15)
% hold on
% plot(log(1/betajend),log(kappaend),"*","Color","black","MarkerSize",4)
xlim([0 1.5*aaalinear(end,1)])
ylim([0.03 1.5*aaalinear(end,2)])
%titlestr1 = 'Phase diagram, log-log scale';
titlestr1 = append('Phase diagram ($l_{nz}$ =', num2str(lnz,'%.4g'), ', $l_{zz}$ = ', num2str(lzz,'%.4g'), '), low temperatures');
title(titlestr1,'Interpreter','latex')
text(0.0002,0.08,'polarized phase','FontSize', 16)
text(0.0006,0.06,'chaotic phase','FontSize', 16)
xlabel('$1/(\beta \mathbf{J} )$','Interpreter','latex')
ylabel('$\kappa$','Interpreter','latex')
legstr11 = append('$\kappa=',num2str(p(1),'%.4f'),' (1/\beta \mathbf{J})$ + ', num2str(p(2),'%.4f'));
legstr12 = 'first-order transition points at low T';
legstr13 ='other first-order transition points'
%legstr14 = 'second-order transition point'
legend(legstr11,legstr12,legstr13,'Interpreter','latex', 'Location', 'southeast','FontSize', 16)
grid on
%%
figure;
subplot(1,2,1)
plot(log(pltx2), log(p(1)*pltx2+ p(2)),'-','Color','Blue');
hold on
plot(log(aaalinear(:,1)),log(aaalinear(:,2)),"o",'Color','Red',"MarkerSize",4)
hold on
plot(log(aaaremain(:,1)),log(aaaremain(:,2)),"o","MarkerSize",4)
% hold on
% plot(log(1/betajend),log(kappaend),"*","Color","black","MarkerSize",4)
xlim([1.5*log(aaalinear(end,1)), -3])
ylim([1.5*log(aaalinear(end,2)),-0])
%titlestr1 = 'Phase diagram, log-log scale';
titlestr1 = append('Phase diagram ($l_{nz}$ =', num2str(lnz,'%.4g'), ', $l_{zz}$ = ', num2str(lzz,'%.4g'), '), low temperatures');
title(titlestr1,'Interpreter','latex')
%text(0.2,0.08,'non-isotropic SYK phase','FontSize', 16)
%text(0.6,0.05,'SYK phase','FontSize', 16)
xlabel('$\log 1/(\beta \mathbf{J} )$','Interpreter','latex')
ylabel('$\log \kappa$','Interpreter','latex')
legstr11 = append('$\log \kappa= \log [',num2str(p(1),'%.4f'),' (1/\beta \mathbf{J})$ + ', num2str(p(2),'%.4f'),']');
legstr12 = 'first-order transition points at low T';
legstr13 ='other first-order transition points'
%legstr14 = 'second-order transition point'
legend(legstr11,legstr12,legstr13,'Interpreter','latex', 'Location', 'southeast')
set(gca,'FontSize',14)
subplot(1,2,2)
plot(log(pltx2), log(p(1)*pltx2),'-','Color','Blue');
hold on
plot(log(aaalinear(:,1)),log(aaalinear(:,2)-p(2)),"o",'Color','Red',"MarkerSize",4)
hold on
plot(log(aaaremain(:,1)),log(aaaremain(:,2)-p(2)),"o","MarkerSize",4)
% hold on
% plot(log(1/betajend),log(kappaend),"*","Color","black","MarkerSize",4)
xlim([1.2*log(aaalinear(end,1)), -4])
ylim([2*log(aaalinear(end,2)),0])
%titlestr1 = 'Phase diagram, log-log scale';
titlestr1 = append('Phase diagram ($l_{nz}$ =', num2str(lnz,'%.4g'), ', $l_{zz}$ = ', num2str(lzz,'%.4g'), '), low temperatures');
title(titlestr1,'Interpreter','latex')
text(0.2,0.08,'non-isotropic SYK phase','FontSize', 16)
text(0.6,0.05,'SYK phase','FontSize', 16)
xlabel('$\log 1/(\beta \mathbf{J} )$','Interpreter','latex')
ylabel('$\log (\kappa - \kappa_{0,fit})$','Interpreter','latex')
legstr11 = append('$\log (\kappa - ', num2str(p(2),'%.4f'),' ) =\log [',num2str(p(1),'%.4f'),' (1/\beta \mathbf{J})$ ]');
legstr12 = 'first-order transition points at low T';
legstr13 ='other first-order transition points'
%legstr14 = 'second-order transition point'
legend(legstr11,legstr12,legstr13,'Interpreter','latex', 'Location', 'southeast')
set(gca,'FontSize',14)
%%
% interinverse= @(x) interp1(1./aaa(:,1),aaa(:,2),x,'spline','extrap')
%
% pltxinverse = linspace(13.5,300,100);
% plotdatinverse = interinverse(pltxinverse);
% figure
% plot(pltx,plotdat, aaa(:,1),aaa(:,2),"o")
% xlim([0 1/12])
% ylim([0 .6])
% xlabel('1/(\beta J)')
% ylabel('k')
% plot(1./pltxinverse,plotdatinverse, aaa(:,1),aaa(:,2),"o")
%%
% interinverse= @(x) interp1(1./aaa(:,1),aaa(:,2),x,'spline','extrap')
%
% pltxinverse = linspace(13.5,160,100);
% plotdatinverse = interinverse(pltxinverse);
%
% figure
% plot(pltxinverse,plotdatinverse, 1./aaa(:,1),aaa(:,2),"o")
% xlim([10, 160])
% ylim([0 1])
% xlabel('\beta J')
% ylabel('k')