Domain-wall renormalization-group study of the three-dimensional random Ising model at finite temperature

1985 ◽  
Vol 31 (1) ◽  
pp. 340-341 ◽  
Author(s):  
W. L. McMillan
Keyword(s):  
Renormalization Group ◽  
Ising Model ◽  
Domain Wall ◽  
Finite Temperature ◽  
Three Dimensional ◽  
Random Ising Model

scholarly journals CRITICAL TEMPERATURE AND AMPLITUDE RATIOS FROM A FINITE TEMPERATURE RENORMALIZATION GROUP

1995 ◽  
Vol 10 (23) ◽  
pp. 3343-3358 ◽  
Author(s):  
M.A. VAN EIJCK ◽  
DENJOE O’CONNOR ◽  
C.R. STEPHENS
Keyword(s):  
Renormalization Group ◽  
Critical Temperature ◽  
Finite Temperature ◽  
Flow Parameter ◽  
Three Dimensional ◽  
Zero Temperature ◽  
Amplitude Ratios ◽  
Flow Equations ◽  
Infrared Divergences ◽  
Good Agreement

We study λφ4 theory using an environmentally friendly finite temperature renormalization group. We derive flow equations, using a fiducial temperature as flow parameter, develop them perturbatively in an expansion free from ultraviolet and infrared divergences, then integrate them numerically from zero to temperatures above the critical temperature. The critical temperature, at which the mass vanishes, is obtained by integrating the flow equations, and is determined as a function of the zero temperature mass and coupling. We calculate the field expectation value and the minimum of the effective potential as functions of temperature and derive some universal amplitude ratios which connect the broken and symmetric phases of the theory. The latter are found to be in good agreement with those of the three-dimensional Ising model obtained from high and low temperature series expansions.

Phase Diagram of Three-Dimensional Site-Random Ising Model

1997 ◽  
Vol 66 (1) ◽  
pp. 215-223 ◽  
Author(s):  
Koji Hukushima ◽  
Yoshihiko Nonomura ◽  
Yukiyasu Ozeki ◽  
Hajime Takayama
Keyword(s):  
Phase Diagram ◽  
Ising Model ◽  
Three Dimensional ◽  
Random Ising Model

scholarly journals DOMAIN WALL RENORMALIZATION GROUP ANALYSIS OF TWO-DIMENSIONAL ISING MODEL

2009 ◽  
Vol 23 (18) ◽  
pp. 3739-3751 ◽  
Author(s):  
KEN-ICHI AOKI ◽  
TAMAO KOBAYASHI ◽  
HIROSHI TOMITA
Keyword(s):  
Renormalization Group ◽  
Ising Model ◽  
Domain Wall ◽  
Domain Walls ◽  
Group Analysis ◽  
Coarse Graining ◽  
Group Method ◽  
Two Dimensional ◽  
Renormalization Group Analysis ◽  
Renormalization Transformation

Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the two-dimensional square lattice. For the lowest-order approximation with two-domain wall states, it realizes the idea of coarse graining of domain walls. We write down explicit analytic renormalization transformation and prove that the picture of the coarse graining of the physical domain walls does hold for all physical renormalization group flows. We solve it to get the fixed point structure and obtain the critical exponents and the critical temperature. These results are very near to the exact values. We also briefly report the improvement using four-domain wall states.

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