Monte Carlo Renormalization Group Analysis of Lattice ${\varphi }^4$ Model in $D=3,4$

Abstract

We present a simple, sophisticated method to capture renormalization group flow in Monte Carlo simulation, which provides important information of critical phenomena. We applied the method to $D=3,4$ lattice ${\varphi }^4$ model and obtained renormalization flow diagram which well reproduces theoretically predicted behavior of continuum ${\varphi }^4$ model. We also show that the method can be easily applied to much more complicated models, such as frustrated spin models.

Comments: 13 pages, revtex, 7 figures. v1:Submitted to PRE. v2:considerably reduced redundancy of presentation. v3:final version to appear in Phys.Rev.E