The Phase Diagram of Scalar Field Theory on the Fuzzy Disc

TL;DR

This paper uses a new bootstrapping method to analyze the phase diagram of scalar field theory on the fuzzy disc, identifying three phases and phase transitions, with analytical insights into transition ratios at large couplings.

Contribution

It introduces a novel bootstrapping approach to determine the phase diagram of scalar field theory on the fuzzy disc, including analytical results for transition ratios.

Findings

Three distinct phases identified

Second and third order phase transitions observed

Analytical ratio of coupling constants at transition derived

Abstract

Using a recently developed bootstrapping method, we compute the phase diagram of scalar field theory on the fuzzy disc with quartic even potential. We find three distinct phases with second and third order phase transitions between them. In particular, we find that the second order phase transition happens approximately at a fixed ratio of the two coupling constants defining the potential. We compute this ratio analytically in the limit of large coupling constants. Our results qualitatively agree with previously obtained numerical results.