FK-DLR properties of a quantum multi-type bose-gas with a repulsive interaction

TL;DR

This paper generalizes FK-DLR properties to multi-type quantum Bose gases with repulsive interactions, proving compactness of finite-volume states and translation invariance of limit states in two dimensions.

Contribution

It extends previous results to multi-type particles with non-negative interactions, establishing compactness and translation invariance of FK-DLR states.

Findings

Finite-volume Gibbs states form a compact family in the thermodynamic limit.

Any limit-point FK-DLR state in two dimensions is translation-invariant.

Abstract

The paper extends earlier results from \cite{SK}, \cite{SKS} about infinite-volume quantum bosonic states (FK-DLR states) to the case of multi-type particles with non-negative interactions. (An example is a quantum Widom--Rowlinson model.) Following the strategy from \cite{SK}, \cite{SKS}, we establish that, for the values of fugacity $z\in (0,1)$ and inverse temperature $\beta >0$, finite-volume Gibbs states form a compact family in the thermodynamic limit. Next, in dimension two we show that any limit-point state (an FK-DLR state in the terminology adopted in \cite{SK}, \cite{SKS}) is translation-invariant.