费米子格点系统的平衡态统计力学
Equilibrium Statistical Mechanics of Fermion Lattice Systems
摘要：
我们研究了费米子晶格系统的平衡态统计力学，由于不相交区域的局部代数的非交换性，与自旋晶格系统相比，费米子晶格系统需要不同的处理。我们的主要结果是等价的KMS条件和变分原理与最小假设的动力学和没有任何明确的假设的潜力。它也适用于自旋晶格系统，产生了巨大的改进，在已知的结果。所有的公式都是用一个费米子（CAR）代数的C ~*-动力学系统来表示的，并具有以下全部或部分假设：（I）相互作用关于费米子数是偶数。（当假设以下（IV）时自动满足。）(II)代数的所有严格局部元素都有一阶时间导数。(III)（II）中的时间导数决定了动力学。(IV)相互作用是晶格平移不变的。一个主要的技术工具是条件期望从全代数到局部子代数的任何有限子集的格，这导致系统的交换平方。这种技术克服了费米子系统张量积结构的缺乏，甚至简化了许多已知的自旋晶格系统的参数。
英文摘要：
We study equilibrium statistical mechanics of Fermion lattice systems which require a different treatment compared with spin lattice systems due to the non-commutativity of local algebras for disjoint regions. Our major result is the equivalence of the KMS condition and the variational principle with a minimal assumption for the dynamics and without any explicit assumption on the potential. It holds also for spin lattice systems as well, yielding a vast improvement over known results. All formulations are in terms of a C*-dynamical systems for the Fermion (CAR) algebra with all or a part of the following assumptions: (I) The interaction is even with respect to the Fermion number. (Automatically satisfied when (IV) below is assumed.) (II) All strictly local elements of the algebra have the first time derivative. (III) The time derivatives in (II) determine the dynamics. (IV) The interaction is lattice translation invariant. A major technical tool is the conditional expectation from the total algebra onto the local subalgebra for any finite subset of the lattice, which induces a system of commuting squares. This technique overcomes the lack of tensor product structures for Fermion systems and even simplifies many known arguments for spin lattice systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
