Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase

TL;DR

This paper analytically examines fluctuation distributions in unfrustrated models like random walks, scalar fields, and the 2d XY model, exploring their relation to effective temperature concepts beyond linear response.

Contribution

It provides a detailed analytical study of fluctuation distributions and ratios in unfrustrated models, extending the fluctuation-dissipation framework beyond linear order.

Findings

Fluctuation distributions are characterized analytically in the studied models.

Ratios of composite operators reveal insights into effective temperature relevance.

Numerical simulations of clock models support the analytical results.

Abstract

We study analytically the distribution of fluctuations of the quantities whose average yield the usual two-point correlation and linear response functions in three unfrustrated models: the random walk, the $d$ dimensional scalar field and the 2d XY model. In particular we consider the time dependence of ratios between composite operators formed with these fluctuating quantities which generalize the largely studied fluctuation-dissipation ratio, allowing us to discuss the relevance of the effective temperature notion beyond linear order. The behavior of fluctuations in the aforementioned solvable cases is compared to numerical simulations of the 2d clock model with $p=6,12$ states.