Confinement in the q-state Potts model

an RG-TCSA study

M. Lencsés, G. Takács

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Abstract: In the ferromagnetic phase of the q-state Potts model, switching on an external magnetic field induces confinement of the domain wall excitations. For the Ising model (q = 2) the spectrum consists of kink-antikink states which are the analogues of mesonic states in QCD, while for q = 3, depending on the sign of the field, the spectrum may also contain three-kink bound states which are the analogues of the baryons. In recent years the resulting “hadron” spectrum was described using several different approaches, such as quantum mechanics in the confining linear potential, WKB methods and also the Bethe-Salpeter equation. Here we compare the available predictions to numerical results from renormalization group improved truncated conformal space approach (RG-TCSA). While mesonic states in the Ising model have already been considered in a different truncated Hamiltonian approach, this is the first time that a precision numerical study is performed for the 3-state Potts model. We find that the semiclassical approach provides a very accurate description for the mesonic spectrum in all the parameter regime for weak magnetic field, while the low-energy expansion from the Bethe-Salpeter equation is only valid for very weak fields where it gives a slight improvement over the semiclassical results. In addition, we confirm the validity of the recent predictions for the baryon spectrum obtained from solving the quantum mechanical three-body problem.

Original languageEnglish
Article number146
JournalJournal of High Energy Physics
Volume2015
Issue number9
DOIs
Publication statusPublished - Sep 29 2015

Fingerprint

Bethe-Salpeter equation
Ising model
baryons
analogs
three body problem
predictions
magnetic fields
confining
domain wall
quantum mechanics
quantum chromodynamics
expansion
excitation
energy

Keywords

  • Exact S-Matrix
  • Field Theories in Lower Dimensions
  • Integrable Field Theories

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Confinement in the q-state Potts model : an RG-TCSA study. / Lencsés, M.; Takács, G.

In: Journal of High Energy Physics, Vol. 2015, No. 9, 146, 29.09.2015.

Research output: Contribution to journalArticle

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