The renormalization group analysis of the spin-spin correlation function in the two-dimensional Ising model

1991 ◽  
Vol 352 (3) ◽  
pp. 601-615 ◽  
Author(s):  
Hidenori Sonoda
Keyword(s):  
Correlation Function ◽  
Renormalization Group ◽  
Ising Model ◽  
Group Analysis ◽  
Spin Correlation ◽  
Two Dimensional ◽  
Renormalization Group Analysis ◽  
Spin Correlation Function

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.

Calculating the conformal charge from the second moment of the spin–spin correlation function

1993 ◽  
Vol 442 (1915) ◽  
pp. 485-488 ◽  
Keyword(s):  
Correlation Function ◽  
Ising Model ◽  
High Field ◽  
Central Charge ◽  
Spin Correlation ◽  
Two Dimensional ◽  
Extrapolation Methods ◽  
Amplitude Ratios ◽  
Spin Correlation Function ◽  
Second Moment

We develop high field expansions for the second moment of the spin–spin correlation function of the two-dimensional Ising model at arbitrary temperature T . Setting T = T c and approaching the critical point along the field direction, this quantity has a 1/ h 2 , divergence as the external field h goes to zero. The amplitude for this divergence is estimated by series extrapolation methods, and is shown to lead to an estimate for the central charge of 0.50 by using Cardy’s formula for the central charge in terms of hyperuniversal amplitude ratios.

RENORMALIZATION GROUP ANALYSIS OF THE ISING MODEL ON TWO-DIMENSIONAL QUASI-LATTICES

1988 ◽  
Vol 02 (01) ◽  
pp. 13-35 ◽  
Author(s):  
HIDEAKI AOYAMA ◽  
TAKASHI ODAGAKI
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Critical Temperature ◽  
Ising Model ◽  
Group Analysis ◽  
Critical Index ◽  
Two Dimensional ◽  
Renormalization Group Analysis

We present a renormalization group analysis of the two-dimensional Ising model on both the Kite-Dart and Rhombi Penrose lattices in which spins are located at the vertices of the lattice. We demonstrate the existence of the phase transition and obtain the critical temperature and the thermal critical index. The thermal critical index is found to be close to unity.

Sign in / Sign up

Export Citation Format

Share Document