%% Draw the RG flow with coordinate-transformed 2-loop RG, for d=6.005 function []=figure3b() dt=0.00001; % 0.00001 timestep in production (overkill) n=0; % number of replicas direction_sign=(-1); % forward=IR=-1, backward=UV=+1 d=6.005; % number of spatial dimension lambda1=-0.55; lambda2=0; % coordinate deformation parameters gI_guessS=3.5813; gII_guessS=4.2788; % guesses for the two-loop fixed point values for d=6.005, lambda1=-0.55, lambda2=0 a=(1931/576); b=(3/2)+(d-6)*(lambda1+(7/4)*lambda2); c=-(d-6)/2; gI_starU=0; gII_starU=sqrt((-b+sqrt(b^2-4*a*c))/(2*a)); % exact values for the fixed point ``U" (in Moore-Read notation) gI_guessZ=0.399*sqrt(d-6); gII_guessZ=0.028*sqrt(d-6); % guess for the fixed point ``Z" (in Moore-Read notation) gI_initials= [0, gI_starU-0.01, gI_starU-0.002,gI_starU+0.001,gI_starU-0.01, gI_starU+0.01, 7.05]; % initial conditions for gI gII_initials=[gII_starU+0.03,gII_starU+0.04, gII_starU+0.04,gII_starU+0.09,gII_starU-0.01678160,gII_starU+0.0693,10]; % initial conditions for gII where_to_put_vectors=[3,1,1.8,8,100,100,100]; Nt_max=200/dt; % stop the trajectory when number of step reaches this number length_max=100; % stop the trajectory when the length of the trajectory reaches this number %% Plot close all figure() hold on % Get the combinatorial factors [S,a1,a2]=combinatorial_factors(n); % Plot Gaussian fixed point scatter3(0,0,1,100,[1,0,0],'filled') % Plot the unstable fixed point, ``U" scatter3(gI_starU,gII_starU,1,100,[0,0.8,0],'filled') % Find and plot the nontrivial fixed point [gI_starS,gII_starS,~]=fixed_point_locater_with_Hessian(n,d,gI_guessS,gII_guessS,lambda1,lambda2); scatter3(gI_starS,gII_starS,1,100,[0,0,1],'filled') % Find and plot the two-direction-unstable fixed point, ``Z," that is visible already at one-loop [gI_starZ,gII_starZ,~]=fixed_point_locater_with_Hessian(n,d,gI_guessZ,gII_guessZ,lambda1,lambda2); scatter3(gI_starZ,gII_starZ,1,100,[0,0.8,0],'filled') % RG flow N_flow=size(gI_initials,2); xx=zeros(1,N_flow-3); yy=zeros(1,N_flow-3); vx=zeros(1,N_flow-3); vy=zeros(1,N_flow-3); i_vec=0; for i_flow=1:N_flow % Set the initial condition gs=[gI_initials(i_flow);gII_initials(i_flow)]; length=0; Nt=1; gI_trajectory=gs(1); gII_trajectory=gs(2); length_vercor=where_to_put_vectors(i_flow); put_vector_flag=0; while(Nt<=Nt_max && lengthlength_vercor) && (put_vector_flag==0) && (i_flow