Renormalization Group results for lattice surface models

TL;DR

This paper applies the lower bound renormalization group to study phase transitions in lattice surface models, connecting Ising and gauge systems, and compares results with previous numerical findings.

Contribution

It introduces a renormalization group approach to analyze phase diagrams of lattice surface models, including open and closed interfaces, with focus on Ising-like transitions.

Findings

Identified phase transition points between different surface phases.

Compared RG results with previous numerical studies.

Discussed limitations of the LBRG method in non-ferromagnetic regions.

Abstract

We study the phase diagram of statistical systems of closed and open interfaces built on a cubic lattice. Interacting closed interfaces can be written as Ising models, while open surfaces as Z(2) gauge systems. When the open surfaces reduce to closed interfaces with few defects, also the gauge model can be written as an Ising spin model. We apply the lower bound renormalization group (LBRG) transformation introduced by Kadanoff (Phys. Rev. Lett. 34, 1005 (1975)) to study the Ising models describing closed and open surfaces with few defects. In particular, we have studied the Ising-like transition of self-avoiding surfaces between the random-isotropic phase and the phase with broken global symmetry at varying values of the mean curvature. Our results are compared with previous numerical work. The limits of the LBRG transformation in describing regions of the phase diagram where not ferromagnetic ground-states are relevant are also discussed.