Finite-size effects of linear sigma model in compactified space–time
The finite-sized effect caused by compactified space–time is scrutinized by means of the linear sigma model with constituent quarks at finite temperature T and chemical potential μ, where the compactified spatial dimension with length L is taken along the Oz direction. We find several finite-size effects associated with compactified length L: (a) There are two types of Casimir energy corresponding to two types of quarks, untwisted and twisted quarks. (b) For untwisted quarks, a first-order phase transition emerges at intermediate values of L when the Casimir effect is not taken into account and is enhanced by Casimir energy at small L. (c) For twisted quarks, the phase transition is cross-over everywhere when μ≤200 MeV . When μ> 200 MeV there occurs a first-order phase transition at large L and becomes cross-over at smaller L.