The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: strongly associating fluids and biased Monte Carlo

TL;DR

This paper explores the calculation of topological susceptibility in the interacting instanton liquid model at finite temperature, focusing on Monte Carlo simulation techniques and the fluid-like behavior of the system with light quarks.

Contribution

It introduces biased Monte Carlo methods to address technical challenges in simulating the IILM, highlighting its fluid-like properties for light quarks.

Findings

IILM behaves as a strongly associating fluid for light quarks.

Biased Monte Carlo techniques can effectively handle simulation complexities.

The study provides a framework for more accurate topological susceptibility calculations.

Abstract

This is the second in a series of papers that investigates the topological susceptibility in the interacting instanton liquid model (IILM) at finite temperature, and deals with the technical issues relating to the Monte Carlo simulations. The IILM reduces field theory to a molecular dynamics description, and for `physical' quark masses the system behaves like a strongly associating fluid. We will argue that this is a generic feature for very light Dirac quark in a non-trivial background, described in the semi-classical approach. To get rid of unnecessary complications, we will present the ideas of biased Monte Carlo, and implement the transition probabilities, for a toy model.