arXiv subjects

Yoshihito Hotta

Publications and source records attributed to Yoshihito Hotta.

3 recordsLinked to original sources

arXiv2015

Tensor-network algorithm for nonequilibrium relaxation in the thermodynamic limit

We propose a tensor-network algorithm for discrete-time stochastic dynamics of a homogeneous system in the thermodynamic limit. We map a $d$-dimensional nonequilibrium Markov process to a $(d+1)$-dimensional infinite tensor network by using a higher-order singular-value decomposition. As an application of the algorithm, we compute the nonequilibrium relaxation from a fully magnetized state to equilibrium of the one- and two- dimensional Ising models with periodic boundary conditions. Utilizing the translational invariance of the systems, we analyze the behavior in the thermodynamic limit directly. We estimated the dynamical critical exponent $z=2.16(5)$ for the two-dimensional Ising model. Our approach fits well with the framework of the nonequilibrium-relaxation method. Our algorithm can compute time evolution of the magnetization of a large system precisely for a relatively short period. In the nonequilibrium-relaxation method, on the other hand, one needs to simulate dynamics of a large system for a short time. The combination of the two provides a new approach to the study of critical phenomena.

cond-mat.stat-mech↗

arXiv2014

Self-Avoiding Walk on Fractal Complex Networks: Exactly Solvable Cases

We study the self-avoiding walk on complex fractal networks called the (u,v)-flower by mapping it to the N-vector model in a generating function formalism. First, we analytically calculate the critical exponent ν and the connective constant by a renormalization-group analysis in arbitrary fractal dimensions. We find that the exponent ν is equal to the displacement exponent, which describes the speed of diffusion in terms of the shortest distance. Second, by obtaining an exact solution for the (u,u)-flower, we provide an example which supports the conjecture that the universality class of the self-avoiding walk on graphs is not determined only by the fractal dimension.

cond-mat.stat-mech↗

arXiv2014

Scaling Concepts in Graph Thoery: Self-Avoiding Walk on Fractal Complex Networks

It was discovered a few years ago that many networks in the real world exhibit self-similarity. A lot of researches on the structures and processes on real and artificial fractal complex networks have been done, drawing an analogy to critical phenomena. However, the non-Markovian dynamics on fractal networks has not been understood well yet. We here study the self-avoiding walk on complex fractal networks through the mapping of the self-avoiding walk to the n-vector model by a generating function formalism. First, we analytically calculate the critical exponent ν and the effective coordination number (the connective constant) by a renormalization-group analysis in various fractal dimensions. We find that the exponent ν is equal to the exponent of displacement, which describes the speed of diffusion in terms of the shortest distance. Second, by obtaining an exact solution, we present an example which supports the well-known conjecture that the universality class of the self-avoiding walk is not determined only by a fractal dimension. Our finding suggests that the scaling theory of polymers can be applied to graphs which lack the Euclidian distance as well. Furthermore, the self-avoiding walk has been exactly solved only on a few lattices embedded in the Euclidian space, but we show that consideration on general graphs can simplify analytic calculations and leads to a better understanding of critical phenomena. The scaling theory of the self-avoiding path will shed light on the relationship between path numeration problems in graph theory and statistical nature of paths.

cond-mat.stat-mech↗