Continuous operation over 1500 h of a PbTe/PbSnTe double-heterostructure laser at 77 K

We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy normalized per lattice site of various multistate spin models in the thermal equilibrium on distinct non-Euclidean surface lattices of the infinite sizes. Whereas the free energy is calculated numerically by means of the corner transfer matrix renormalization group algorithm, the radius of curvature has an analytic expression. Two tasks are considered in this work. First, we search for such a lattice geometry, which minimizes the free energy per site. We conjecture that the only Euclidean flat geometry results in the minimal free energy per site regardless of the spin model. Second, the relations among the free energy, the radius of curvature, and the phase transition temperatures are analyzed. We found out that both the free energy and the phase transition temperature inherit the structure of the lattice geometry and asymptotically approach the profile of the Gaussian radius of curvature. This achievement opens new perspectives in the AdS-CFT correspondence theories.

Section: Introductionmentioning

confidence: 99%

Free-energy analysis of spin models on hyperbolic lattice geometries

Serina¹,

Genzor²,

Lee³

et al. 2016

“…Quantum and statistical phenomena under non-Euclidean geometry have been attracting research interests in a number of physical systems. For example, experiments on magnetic nano-structures [1][2][3] have been performed in connection with soft materials exhibiting a conical geometry [4]. One can list investigations on the quantum gravity [5,6], lattice dislocations of the solidstate crystals, complex networks [7,8] such as neural systems and complicated web connections.…”

Section: Introductionmentioning

confidence: 99%

Mean-field universality class induced by weak hyperbolic curvatures

Gendiar¹,

Daniška²,

Krčmár³

et al. 2014

Order-disorder phase transition of the ferromagnetic Ising model is investigated on a series of twodimensional lattices that have negative Gaussian curvatures. Exceptional lattice sites of coordination number seven are distributed on the triangular lattice, where the typical distance between the nearest exceptional sites is proportional to an integer parameter n. Thus, the corresponding curvature is asymptotically proportional to −n −2 . Spontaneous magnetization and specific heat are calculated by means of the corner transfer matrix renormalization group method. For all the finite n cases, we observe the mean-field-like phase transition. It is confirmed that the entanglement entropy at the transition temperature is linear in (c/6) ln n, where c = 1/2 is the central charge of the Ising model. The fact agrees with the presence of the typical length scale n being proportional to the curvature radius.

“…An increasing interest in the thermodynamic behavior of various physical models on non-Euclidean (curved) surfaces has been persisting for about two decades, due to recent experimental fabrication of soft materials with conical geometry [1] and magnetic nanostructures which exhibit negatively curved geometries [2][3][4]. Curved geometries are also relevant in the theory of quantum gravity [5,6].…”

Section: Introductionmentioning

confidence: 99%

Weak correlation effects in the Ising model on triangular-tiled hyperbolic lattices

Gendiar¹,

Krčmár²,

Andergassen³

et al. 2012

The Ising model is studied on a series of hyperbolic two-dimensional lattices which are formed by tessellation of triangles on negatively curved surfaces. In order to treat the hyperbolic lattices, we propose a generalization of the corner transfer matrix renormalization group method using a recursive construction of asymmetric transfer matrices. Studying the phase transition, the mean-field universality is captured by means of a precise analysis of thermodynamic functions. The correlation functions and the density-matrix spectra always decay exponentially even at the transition point, whereas power-law behavior characterizes criticality on the Euclidean flat geometry. We confirm the absence of a finite correlation length in the limit of infinite negative Gaussian curvature.