Nature of Phase Transitions in a Generalized Complex |psi|^4 Model

TL;DR

This study uses Monte Carlo simulations to explore phase transitions in a generalized complex |psi|^4 model, revealing tunable first-order transitions via a modified Hamiltonian, contrasting with the continuous transitions in the standard model.

Contribution

Introduces a generalized Hamiltonian with a fugacity term to control vortex density, demonstrating the ability to induce strong first-order phase transitions in the complex |psi|^4 theory.

Findings

Standard model exhibits continuous XY-like transitions.

Modified model can undergo strong first-order phase transitions.

Mean-field approximation does not apply to the standard formulation.

Abstract

We employ Monte Carlo simulations to study a generalized three-dimensional complex $psi|^4 theory of Ginzburg-Landau form and compare our numerical results with a recent quasi-analytical mean-field type approximation, which predicts first-order phase transitions in parts of the phase diagram. As we have shown earlier, this approximation does not apply to the standard formulation of the model. This motivated us to introduce a generalized Hamiltonian with an additional fugacity term controlling implicitly the vortex density. With this modification we find that the complex |psi|^4 theory can, in fact, be tuned to undergo strong first-order phase transitions. The standard model is confirmed to exhibit continuous transitions which can be characterized by XY model exponents, as expected by universality arguments. A few remarks on the two-dimensional case are also made.