The Phase Diagram of Four Flavor SU(2) Lattice Gauge Theory at Nonzero Chemical Potential and Temperature

TL;DR

This study explores the phase transitions of four-flavor SU(2) lattice gauge theory at varying chemical potential and temperature, revealing second order and first order transitions, a tricritical point, and consistency with effective theory predictions.

Contribution

It provides the first detailed lattice simulation of the phase diagram for four-flavor SU(2) gauge theory at nonzero chemical potential and temperature, confirming theoretical predictions.

Findings

Second order phase transition to diquark condensate at zero T

Line of second order transitions at low T with increasing chemical potential

First order transitions from diquark to quark-gluon plasma at high T

Abstract

SU(2) lattice gauge theory with four flavors of quarks is simulated at nonzero chemical potential $\mu$ and temperature $T$ and the results are compared to the predictions of Effective Lagrangians. Simulations on $16^4$ lattices indicate that at zero $T$ the theory experiences a second order phase transition to a diquark condensate state. Several methods of analysis, including equation of state fits suggested by Chiral Perturbation Theory, suggest that mean-field scaling describes this critical point. Nonzero $T$ and $\mu$ are studied on $12^3 \times 6$ lattices. For low $T$, increasing $\mu$ takes the system through a line of second order phase transitions to a diquark condensed phase. Increasing $T$ at high $\mu$, the system passes through a line of first order transitions from the diquark phase to the quark-gluon plasma phase. Metastability is found in the vicinity of the first order line. There is a tricritical point along this line of transitions whose position is consistent with theoretical predictions.