Confinement in the tricritical Ising model

TL;DR

This paper investigates magnetic perturbations in the tricritical Ising model, revealing confinement phenomena, meson spectra, and novel features due to vacuum degeneracy, with results validated by finite volume spectrum analysis.

Contribution

It extends semi-classical methods to analyze confinement and meson spectra in the tricritical Ising model under magnetic perturbations, including novel vacuum degeneracy effects.

Findings

Magnetic perturbations cause confinement of kinks in the model.

Semi-classical spectrum matches finite volume spectrum results.

Vacuum degeneracy leads to unique confinement patterns.

Abstract

We study the leading and sub-leading magnetic perturbations of the thermal $E_7$ integrable deformation of the tricritical Ising model. In the low-temperature phase, these magnetic perturbations lead to the confinement of the kinks of the model. The resulting meson spectrum can be obtained using the semi-classical quantisation, here extended to include also mesonic excitations composed of two different kinks. An interesting feature of the integrable sub-leading magnetic perturbation of the thermal $E_7$ deformation of the model is the possibility to swap the role of the two operators, i.e. the possibility to consider the model as a thermal perturbation of the integrable $\mathcal{A}_3$ model associated to the sub-leading magnetic deformation. Due to the occurrence of vacuum degeneracy unrelated to spontaneous symmetry breaking in $\mathcal{A}_3$, the confinement pattern shows novel features compared to previously studied models. Interestingly enough, the validity of the semi-classical description in terms of the $\mathcal{A}_3$ endpoint extends well beyond small fields, and therefore the full parameter space of the joint thermal and sub-leading magnetic deformation is well described by a combination of semi-classical approaches. All predictions are verified by comparison to finite volume spectrum resulting from truncated conformal space.