A study of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si9.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:math> model in the Tsallis nonextensive statistics

Ishihara, M.

doi:10.1016/j.physa.2011.07.047

Cited by 2 publications

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The linear sigma model is also used to study the phase transition at high energies. The model is the extension of x 4 model, and the effects of the Tsallis statistics was studied in the x 4 model in quantum mechanics [16,17]. The phase transition should be investigated with these models, when the distribution is described with the Tsallis distribution.…”

Section: Introductionmentioning

confidence: 99%

Effects of the Tsallis distribution in the linear sigma model

Ishihara

2015

Int. J. Mod. Phys. E

Self Cite

View full text Add to dashboard Cite

Abstract. The effects of the Tsallis distribution which has two parameters, q and T , on physical quantities are studied using the linear sigma model in chiral phase transitions. The Tsallis distribution approaches the Boltzmann-Gibbs distribution as q approaches 1. The parameter T dependences of the condensate and mass for various q are shown, where T is called temperature. The critical temperature and energy density are described with digamma function, and the q dependences of these quantities and the extension of Stefan-Boltzmann limit of the energy density are shown. The following facts are clarified. The chiral symmetry restoration at q > 1 occurs at low temperature, compared with the restoration at q = 1. The sigma mass and pion mass reflect the restoration. The critical temperature decreases monotonically as q increases. The small deviation from the Boltzmann-Gibbs distribution results in the large deviations of physical quantities, especially the energy density. It is displayed from the energetic point of view that the small deviation from the Boltzmann-Gibbs distribution is realized for q > 1. The physical quantities are affected by the Tsallis distribution even when |q − 1| is small.

show abstract

Section: Introductionmentioning

confidence: 99%

Effects of the Tsallis distribution in the linear sigma model

Ishihara

2015

Int. J. Mod. Phys. E

Self Cite

View full text Add to dashboard Cite

show abstract

Application of optimization method to the x⁴ model in the Tsallis nonextensive statistics

Ishihara

2014

Int. J. Mod. Phys. B

Self Cite

View full text Add to dashboard Cite

We study the effects of the environment described by the Tsallis nonextensive statistics on physical quantities using an optimization method in the case of small deviation from the Boltzmann-Gibbs statistics. The x 4 model is used and the density operator is restricted to be a gaussian form. The variational parameter is the frequency Ω of a particle in the optimization method. We obtain an approximate expression of free energy and of the expectation value of βmΩ 2 x 2 /2, where β is the inverse of the temperature and m is the mass of a particle. Numerically, the optimized frequency is estimated and the expectation value of βmΩ 2 x 2 /2 is calculated. The effects of the Tsallis nonextensive statistic for small deviation from the Boltzmann-Gibbs statistics are found: 1) the frequency modulation of a particle and 2) the variation of the expectation value of βmΩ 2 x 2 /2 at high temperature.

show abstract

A study of the x4 model in the Tsallis nonextensive statistics

Cited by 2 publications

References 14 publications

Effects of the Tsallis distribution in the linear sigma model

Effects of the Tsallis distribution in the linear sigma model

Application of optimization method to the x⁴ model in the Tsallis nonextensive statistics

Contact Info

Product

Resources

About

A study of the x4 model in the Tsallis nonextensive statistics

Cited by 2 publications

References 14 publications

Effects of the Tsallis distribution in the linear sigma model

Effects of the Tsallis distribution in the linear sigma model

Application of optimization method to the x4 model in the Tsallis nonextensive statistics

Contact Info

Product

Resources

About

Application of optimization method to the x⁴ model in the Tsallis nonextensive statistics