# An extended Agassi model: algebraic structure, phase diagram, and large size limit

## TL;DR

This paper extends the Agassi model, exploring its algebraic structure, phase diagram, and large size limit through mean-field and $1/j$ analysis, providing insights into its thermodynamic behavior.

## Contribution

It introduces an algebraic extension of the Agassi model, including its bosonic realization, mean-field analysis, and large size limit study.

## Key findings

- Phase diagram characterized for the extended model
- Ground state energy analyzed in the thermodynamic limit
- Order parameters derived from finite-$j$ diagonalization

## Abstract

The Agassi model is a schematic two-level model that involves pairing and monopole-monopole interactions. It is, therefore, an extension of the well known Lipkin-Meshkov-Glick (LMG) model. In this paper we review the algebraic formulation of an extension of the Agassi model as well as its bosonic realization through the Schwinger representation. Moreover, a mean-field approximation for the model is presented and its phase diagram discussed. Finally, a $1/j$ analysis, with $j$ proportional to the degeneracy of each level, is worked out to obtain the thermodynamic limit of the ground state energy and some order parameters from the exact Hamiltonian diagonalization for finite$-j$.