Stochastic Quantization of the Spherical Model and Supersymmetry

TL;DR

This paper develops a supersymmetric quantum spherical model using stochastic quantization, exploring its critical behavior and phase transitions at different temperatures, and identifying critical dimensions.

Contribution

It introduces a supersymmetric version of the quantum spherical model via stochastic quantization, linking Brownian motion and supersymmetric quantum mechanics.

Findings

The model exhibits classical and quantum phase transitions.

Critical dimensions are determined for the supersymmetric model.

The approach connects stochastic processes with supersymmetry in quantum models.

Abstract

We use the stochastic quantization method to construct a supersymmetric version of the quantum spherical model. This is based on the equivalence between the Brownian motion described by a Langevin equation and the supersymmetric quantum mechanics, which is connected with the existence of the Nicolai map. We investigate the critical behavior of the supersymmetric model at finite as well as at zero temperatures, showing that it exhibits both classical and quantum phase transitions, and determine the critical dimensions.