摘要翻译:
在定义具有长程相互作用的系统的热力学极限方面存在问题;结果,这类体系的热力学行为是反常的。在本工作中,我们从广义和非广义热力学的角度回顾了一些概念。我们使用一个模型,其哈密顿量考虑了在链中通过幂律铁磁耦合的自旋,该幂律在大的粒子间距离$r$as$1/r^{\alpha}$for$\alpha\geq0$时衰减。在这里,我们回顾旧的非扩展缩放。此外,我们还提出了一个新的哈密顿量,其标度为$2\frac{(n/2)^{1-\alpha}-1}{1-\alpha}$,它明确地包含了晶格的对称性和对系统尺寸$n$的依赖关系。新方法使我们能够改进以前的结果。通过蒙特卡罗模拟进行了数值试验。模型中采用周期边界条件来消除表面效应。
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英文标题:
《Thermodynamics from a scaling Hamiltonian》
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作者:
L. A. del Pino, P. Troncoso and S. Curilef
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最新提交年份:
2007
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分类信息:
一级分类:Physics 物理学
二级分类:Statistical Mechanics 统计力学
分类描述:Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变,热力学,场论,非平衡现象,重整化群和标度,可积模型,湍流
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一级分类:Physics 物理学
二级分类:Strongly Correlated Electrons 强关联电子
分类描述:Quantum magnetism, non-Fermi liquids, spin liquids, quantum criticality, charge density waves, metal-insulator transitions
量子磁学,非费米液体,自旋液体,量子临界性,电荷密度波,金属-绝缘体跃迁
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英文摘要:
There are problems with defining the thermodynamic limit of systems with long-range interactions; as a result, the thermodynamic behavior of these types of systems is anomalous. In the present work, we review some concepts from both extensive and nonextensive thermodynamic perspectives. We use a model, whose Hamiltonian takes into account spins ferromagnetically coupled in a chain via a power law that decays at large interparticle distance $r$ as $1/r^{\alpha}$ for $\alpha\geq0$. Here, we review old nonextensive scaling. In addition, we propose a new Hamiltonian scaled by $2\frac{(N/2)^{1-\alpha}-1}{1-\alpha}$ that explicitly includes symmetry of the lattice and dependence on the size, $N$, of the system. The new approach enabled us to improve upon previous results. A numerical test is conducted through Monte Carlo simulations. In the model, periodic boundary conditions are adopted to eliminate surface effects.
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PDF链接:
https://arxiv.org/pdf/710.5644