有限温度下多元场论中的相变
Phase transition in multicomponent field theory at finite temperature
摘要：
在有限温度和密度下的核物质表现出几种相变，这些相变可能发生在宇宙演化的早期阶段，并且可以在重离子或强子-强子碰撞中实现。由于缺乏小参数，相变的微观描述是非常困难的。在这里，我们提出了一个通用的方法，允许治疗的情况下，没有小参数。该方法基于最优微扰理论和自相似近似理论。它允许，从一个渐近小参数的权力发散扰动系列，构造表达式外推渐近级数的参数的任意值，包括其无限极限。这样的逼近的例子是：右根逼近，左根逼近，连根逼近，指数逼近和因子逼近。本文以多分量场论中规范对称性破缺的相变为例说明了这种方法。所发现的临界指数与蒙特卡罗模拟以及复杂的Pade-Borel求和方法非常一致，而我们的方法要简单得多。该方法的一个很好的特点是，它给出了精确的值的情况下，精确的解决方案是已知的。
英文摘要：
Nuclear matter at finite temperature and barion density exhibits several phase transitions that could happen at the early stages of the Universe evolution and could be realized in heavy-ion or hadron-hadron collisions. Microscopic description of phase transitions is notoriously difficult because of the absence of small parameters. Here we present a general approach allowing to treat situations, when there are no small parameters. The approach is based on optimized perturbation theory and self-similar approximation theory. It allows, starting with divergent perturbation series in powers of an asymptotically small parameter, to construct expressions extrapolating asymptotic series to arbitrary values of the parameter, including its infinite limit. Examples of such approximants are: right root approximants, left root approximants, continued root approximants, exponential approximants, and factor approximants. The approach is illustrated by the phase transition of gauge symmetry breaking in a multicomponent field theory. The found critical indices are in very good agreement with Monte Carlo simulations as well as with complicated methods of Pade-Borel summation, while our approach is much simpler. The nice feature of the approach is that it gives exact values for the cases where exact solutions are known.
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