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.

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

References in corpus (4)

• A Monte Carlo study of leading order scaling corrections of phi^4 theory on a three dimensional lattice
• Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model
• Finite Size Scaling and ``perfect'' actions: the three dimensional Ising model
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Cited by in corpus (3)

• Monte Carlo renormalization group study of the Heisenberg and XY antiferromagnet on the stacked triangular lattice and the chiral ${\varphi }^4$ model
• Phase diagram of the three-dimensional Gaussian random field Ising model: A Monte Carlo renormalization-group study
• Finite Size Scaling of the 2D Six-Clock model