The critical region of strong-coupling lattice QCD in different large-N limits

TL;DR

This paper investigates the critical behavior of lattice QCD in the strong-coupling limit across different large-N scenarios, revealing how the critical region's width varies with N_c and N_f, and discussing implications for continuum theories.

Contribution

It provides a detailed analysis of the critical region in strong-coupling lattice QCD for various large-N limits, highlighting the different scaling behaviors and their theoretical implications.

Findings

Critical region has finite width at N_c=∞ for fixed g^2N_c.

Width of critical region scales as 1/N_f^{1/2} for N_f→∞ and N_c=1.

Generalization to higher dimensions and N_c>1 affects the scaling exponent p but not the fundamental behavior.

Abstract

We study the critical behavior at nonzero temperature phase transitions of an effective Hamiltonian derived from lattice QCD in the strong-coupling expansion. Following studies of related quantum spin systems that have a similar Hamiltonian, we show that for large $N_c$ and fixed $g^2N_c$, mean field scaling is not expected, and that the critical region has a finite width at $N_c=\infty$. A different behavior rises for $N_f\to \infty$ and fixed $N_c$ and $g^2/N_f$, which we study in two spatial dimensions and for $N_c=1$. We find that the width of the critical region is suppressed by $1/N_f^p$ with $p=1/2$, and argue that a generalization to $N_c>1$ and to three dimensions will change this only in detail (e.g. the value of $p>0$), but not in principle. We conclude by stating under what conditions this suppression is expected, and remark on possible realizations of this phenomenon in lattice gauge theories in the continuum.