Block model for the XY-type Landau-Ginzburg-Wilson Hamiltonian with an inhomogeneous temperature

TL;DR

This paper investigates phase fluctuations in an XY-type Landau-Ginzburg-Wilson Hamiltonian with inhomogeneous temperature, revealing self-organized block structures coupled as a random-bond XY model, consistent with domain wall calculations.

Contribution

It introduces a block model for the Hamiltonian with inhomogeneous temperature, linking phase fluctuations to self-organized structures and validating couplings with domain wall methods.

Findings

Self-organized blocks form near the saddle point.

Couplings between blocks match domain wall method results.

The model captures phase fluctuation behavior in inhomogeneous systems.

Abstract

The phase fluctuation near the saddle point solution of the XY-type Landau-Ginzburg-Wilson Hamiltonian with random temperature is studied. For the modes with lowest eigenvalue, the systems is self-organized into blocks, which are coupled as a XY model with random bond. The couplings obtained in this way agree with those by domain wall method.