Quenched lattice QCD at finite isospin density and related theories

TL;DR

This paper investigates quenched lattice QCD at finite isospin and related theories, revealing second-order phase transitions with mean-field scaling near critical points, and discusses the implications of the quenched approximation.

Contribution

It demonstrates that quenched approximations for these theories behave similarly to full theories due to real positive fermion determinants, and analyzes critical scaling properties.

Findings

Second-order phase transitions observed

Scaling with mean-field critical exponents

Quenched approximations behave like full theories

Abstract

We study quenched QCD at finite chemical potential, $\mu_I$, for the third component of isospin and quenched two-colour QCD at finite chemical potential, $\mu$, for quark number. In contrast to the quenched approximation to QCD at finite quark-number chemical potential, the quenched approximations to these theories behave similarly to the full theories. The reason is that these theories have real positive fermion determinants. In both of these theories there is some critical chemical potential above which the charge coupled to the chemical potential is spontaneously broken. In each case, the transition appears to be second order. We study the scaling properties near the critical point using scaling functions suggested by effective (chiral) Lagrangians and find evidence for scaling with mean-field critical exponents in each case. The subtleties associated with observing the critical scaling of these theories are discussed.