arXiv 1606.041922016-06-14hep-ph

Tsallis非广延统计下线性西格玛模型中的手征相变

Chiral phase transitions in the linear sigma model in the Tsallis nonextensive statistics

Masamichi Ishihara

备注：: 10 pages, 6 figures
发表信息：: International Journal of Modern Physics E 25, 1650066 (2016)
DOI：: 10.1142/S021830131650066X

摘要：

我们研究了Tsallis非广延统计中的手征相变，该统计有两个参数，温度$T$和熵参数$q$ .本研究采用线性西格玛模型。在无质量自由粒子近似下计算了临界温度、凝聚态、质量和能量密度。临界温度随着$q$的增加而降低。在$q>1$处的冷凝物小于在$q=1$处的冷凝物。在高温下，$q>1$处的σ质量比$q=1$处的质量重，而在低温下，$q>1$处的σ质量比$q=1$处的质量轻。$q>1$的π介子质量比$q=1$的质量重。能量密度随着$q$的增加而显著增加。在$q$ -期望值的情况下的$q$依赖性弱于在具有Tsallis分布的传统期望值的情况下的依赖性。从能量的角度来看，参数$q$应小于$4/3$。Tsallis统计量的有效性可以通过当相互作用较弱时对$5/4 < q < 4/3$的限制的$q$的差异来确定，因为在具有Tsallis分布的常规期望值的情况下，参数$q$小于$5/4$。

英文摘要：

We studied chiral phase transitions in the Tsallis nonextensive statistics which has two parameters, the temperature $T$ and entropic parameter $q$. The linear sigma model was used in this study. The critical temperature, condensate, masses, and energy density were calculated under the massless free particle approximation. The critical temperature decreases as $q$ increases. The condensate at $q>1$ is smaller than that at $q=1$. The sigma mass at $q>1$ is heavier than the mass at $q=1$ at high temperature, while the sigma mass at $q>1$ is lighter than the mass at $q=1$ at low temperature. The pion mass at $q>1$ is heavier than the mass at $q=1$. The energy density increases remarkably as $q$ increases. The $q$ dependence in the case of the $q$-expectation value is weaker than that in the case of the conventional expectation value with a Tsallis distribution. The parameter $q$ should be smaller than $4/3$ from energetic point of view. The validity of the Tsallis statistics can be determined by the difference in $q$ of the restriction for $5/4 < q < 4/3$ when the interaction is weak, because the parameter $q$ is smaller than $5/4$ in the case of the conventional expectation value with a Tsallis distribution.

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