Disordered $\lambda\varphi^{4}+\rho\varphi^{6}$ Landau-Ginzburg model

TL;DR

This paper analyzes a disordered Landau-Ginzburg model with $ ext{lambda} ext{phi}^4 + ext{rho} ext{phi}^6$ interactions, revealing multiple ground states, metastability, and performing a one-loop renormalization beyond mean-field approximation.

Contribution

It introduces a novel analysis of the disordered $ ext{lambda} ext{phi}^4 + ext{rho} ext{phi}^6$ model using replica symmetry and one-loop renormalization, extending mean-field results.

Findings

Multiple ground states with different order parameters identified.

Presence of metastable equilibrium states at low temperatures.

One-loop renormalization performed beyond mean-field approximation.

Abstract

We discuss a disordered $\lambda\varphi^{4}+\rho\varphi^{6}$ Landau-Ginzburg model defined in a d-dimensional space. First we adopt the standard procedure of averaging the disorder dependent free energy of the model. The dominant contribution to this quantity is represented by a series of the replica partition functions of the system. Next, using the replica symmetry ansatz in the saddle-point equations, we prove that the average free energy represents a system with multiple ground states with different order parameters. For low temperatures we show the presence of metastable equilibrium states for some replica fields for a range of values of the physical parameters. Finally, going beyond the mean-field approximation, the one-loop renormalization of this model is performed, in the leading order replica partition function.