Critical Behaviour of the Fuzzy Sphere

TL;DR

This paper investigates the phase transition of a multi-matrix model with a fuzzy sphere phase, analyzing finite size scaling and critical exponents through theoretical predictions and Monte Carlo simulations.

Contribution

It provides the first detailed finite size scaling analysis of the fuzzy sphere evaporation transition, confirming theoretical critical exponents with numerical simulations.

Findings

Critical exponents match theoretical predictions within error margins.

Specific heat peak scales with an exponent of approximately 2/3.

Finite size scaling collapse supports the proposed scaling ansatz.

Abstract

We study a multi-matrix model whose low temperature phase is a fuzzy sphere that undergoes an evaporation transition as the temperature is increased. We investigate finite size scaling of the system as the limiting temperature of stability of the fuzzy sphere phase is approached. We find on theoretical grounds that the system should obey scaling with specific heat exponent \alpha=1/2, shift exponent \bar \lambda=4/3 and that the peak in the specific heat grows with exponent \bar \omega=2/3. Using hybrid Monte Carlo simulations we find good collapse of specific heat data consistent with a scaling ansatz which give our best estimates for the scaling exponents as \alpha=0.50 \pm 0.01,\bar \lambda=1.41 \pm 0.08 and \bar \omega=0.66 \pm 0.08 .