Fluctuation-Induced Forces in Disordered Landau-Ginzburg Model

TL;DR

This paper investigates fluctuation-induced forces in a disordered Landau-Ginzburg model, analyzing how boundary conditions and disorder influence the sign and magnitude of these forces through spectral zeta-function methods.

Contribution

It introduces a series representation for the quenched free energy and evaluates boundary-induced forces considering disorder and boundary conditions in a unified spectral framework.

Findings

Fluctuation-induced forces depend non-trivially on disorder strength.

Long-range fluctuations occur at specific disorder levels, affecting boundary sensitivity.

The sign of the force varies with the non-thermal control parameter.

Abstract

We discuss fluctuation-induced forces in a system described by a continuous Landau-Ginzburg model with a quenched disorder field, defined in a $d$-dimensional slab geometry $\mathbb R^{d-1}\times[0,L]$. A series representation for the quenched free energy in terms of the moments of the partition function is presented. In each moment an order parameter-like quantity can be defined, with a particular correlation length of the fluctuations. For some specific strength of the non-thermal control parameter, it appears a moment of the partition function where the fluctuations associated to the order parameter-like quantity becomes long-ranged. In this situation, these fluctuations become sensitive to the boundaries. In the Gaussian approximation, using the spectral zeta-function method, we evaluate a functional determinant for each moment of the partition function. The analytic structure of each spectral zeta-function depending on the dimension of the space for the case of Dirichlet, Neumann Laplacian and also periodic boundary conditions is discussed in a unified way. Considering the moment of the partition function with the largest correlation length of the fluctuations, we evaluate the induced force between the boundaries, for Dirichlet boundary conditions. We prove that the sign of the fluctuation-induced force for this case depend in a non-trivial way on the strength of the non-thermal control parameter.