arXiv subjects

Matej Mosko

Publications and source records attributed to Matej Mosko.

2 recordsLinked to original sources

arXiv2025

Tensor-Network study of Ising model on infinite hyperbolic dodecahedral lattice

We propose a tensor-network-based algorithm to study the classical Ising model on an infinitely large hyperbolic lattice with a regular 3D tesselation of identical dodecahedra. We reformulate the corner transfer matrix renormalization group (CTMRG) algorithm from 2D to 3D to reproduce the known results on the cubic lattice. We subsequently generalize the CTMRG to a hyperbolic lattice with dodecahedral cells, which is an infinite-dimensional lattice. We analyze the spontaneous magnetization, von Neumann entropy, and correlation length to find a continuous non-critical phase transition on the dodecahedral lattice. We estimate the phase-transition temperature and find the magnetic critical exponents $\beta=0.4999$ and $\delta=3.007$, which confirm the mean-field universality class, in accord with predictions from Monte Carlo and high-temperature series expansions. The algorithm can be applied to arbitrary multi-state spin models.

cond-mat.stat-mech↗

arXiv2024

Vertex Representation of Hyperbolic Tensor Networks

We propose a vertex representation of the tensor network (TN) for classical spin systems on hyperbolic lattices. The tensors form a network of regular $p$-sided polygons ($p>4$) with the coordination number four. The response to multi-state spin systems on the hyperbolic TN is analyzed for their entire parameter space. We show that entanglement entropy is sensitive to distinguish various hyperbolic geometries whereas other thermodynamic quantities are not. We test the numerical accuracy of vertex TNs in the phase transitions of the first, second, and infinite order at the point of maximal entanglement entropy. The hyperbolic structure of TNs induces non-critical properties in the bulk although boundary conditions significantly affect the total free energy in the thermodynamic limit. Thus developed vertex-type TN can be used for the lowest-energy quantum states on the hyperbolic lattices.

cond-mat.stat-mech↗