arXiv subjects

Saburo Higuchi

Publications and source records attributed to Saburo Higuchi.

17 recordsLinked to original sources

arXiv2017

Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models

We introduce a novel random walk model that emerges in the event-chain Monte Carlo (ECMC) of spin systems. In the ECMC, the lifting variable specifying the spin to be updated changes its value to one of its interacting neighbor spins. This movement can be regarded as a random walk in a random environment with a feedback. We investigate this random walk numerically in the case of the classical XY model in 1,2, and 3 dimensions to find that it is superdiffusive near the critical point of the underlying spin system. It is suggested that the performance improvement of the ECMC is related to this anomalous behavior.

cond-mat.stat-mech↗

arXiv2016

Extension of the constant exchange probability method to multi-dimensional replica exchange Monte Carlo applied to the tri-critical spin-1 Blume-Capel model

In replica exchange Monte Carlo (REM), tuning of the temperature set and the exchange scheduling are crucial in improving the accuracy and reducing calculation time. In multi-dimensional simulated tempering, the first order phase transition is accessible. Therefore it is important to study the tuning of parameter set and the scheduling of exchanges in the parallel counterpart, the multi-dimensional REM. We extend Hukushima's constant exchange probability method to multi-dimensional REM for the parameter set. We further propose a combined method to use this set and the Bittner-Nussbaumer-Janke's PT tau algorithm for scheduling. We test the proposed method in two-dimensional spin-1 Blume-Capel model and find that it works efficiently, including the vicinity of the first order phase transition.

cond-mat.stat-mech↗

arXiv2016

Monte Carlo estimation of the number of tatami tilings

Motivated by the way Japanese tatami mats are placed on the floor, we consider domino tilings with a constraint and estimate the number of such tilings of plane regions. We map the system onto a monomer-dimer model with a novel local interaction on the dual lattice. We use a variant of the Hamiltonian replica exchange Monte Carlo method and the multi-parameter reweighting technique to study the model. The properties of the quantity are studied beyond exact enumeration and combinatorial method. The logarithm of the number of the tilings is linear in the boundary length of the region for all the regions studied.

cond-mat.stat-mech↗

arXiv2009

Decimation flows in constraint satisfaction problems

We study hard constraint satisfaction problems with a decimation approach based on message passing algorithms. Decimation induces a renormalization flow in the space of problems, and we exploit the fact that this flow transforms some of the constraints into linear constraints over GF(2). In particular, when the flow hits the subspace of linear problems, one can stop decimation and use Gaussian elimination. We introduce a new decimation algorithm which uses this linear structure and shows a strongly improved performance with respect to the usual decimation methods on some of the hardest locked occupation problems.

cond-mat.dis-nn↗

arXiv2009

Susceptibility Propagation for Constraint Satisfaction Problems

We study the susceptibility propagation, a message-passing algorithm to compute correlation functions. It is applied to constraint satisfaction problems and its accuracy is examined. As a heuristic method to find a satisfying assignment, we propose susceptibility-guided decimation where correlations among the variables play an important role. We apply this novel decimation to locked occupation problems, a class of hard constraint satisfaction problems exhibited recently. It is shown that the present method performs better than the standard belief-guided decimation.

cond-mat.dis-nn↗

arXiv1999

Loop Model with Generalized Fugacity in Three Dimensions

A statistical model of loops on the three-dimensional lattice is proposed and is investigated. It is O(n)-type but has loop fugacity that depends on global three-dimensional shapes of loops in a particular fashion. It is shown that, despite this non-locality and the dimensionality, a layer-to-layer transfer matrix can be constructed as a product of local vertex weights for infinitely many points in the parameter space. Using this transfer matrix, the site entropy is estimated numerically in the fully packed limit.

cond-mat.stat-mech↗

arXiv1999

Compact polymers on decorated square lattices

A Hamiltonian cycle of a graph is a closed path that visits every vertex once and only once. It serves as a model of a compact polymer on a lattice. I study the number of Hamiltonian cycles, or equivalently the entropy of a compact polymer, on various lattices that are not homogeneous but with a sublattice structure. Estimates for the number are obtained by two methods. One is the saddle point approximation for a field theoretic representation. The other is the numerical diagonalization of the transfer matrix of a fully packed loop model in the zero fugacity limit. In the latter method, several scaling exponents are also obtained.

cond-mat.stat-mech↗

arXiv1998

Hamiltonian cycles on random lattices of arbitrary genus

A Hamiltonian cycle of a graph is a closed path that visits every vertex once and only once. It has been difficult to count the number of Hamiltonian cycles on regular lattices with periodic boundary conditions, e.g. lattices on a torus, due to the presence of winding modes. In this paper, the exact number of Hamiltonian cycles on a random trivalent fat graph drawn faithfully on a torus is obtained. This result is further extended to the case of random graphs drawn on surfaces of an arbitrary genus. The conformational exponent gamma is found to depend on the genus linearly.

cond-mat.stat-mech↗

arXiv1998

Field theoretic approach to the counting problem of Hamiltonian cycles of graphs

A Hamiltonian cycle of a graph is a closed path that visits each site once and only once. I study a field theoretic representation for the number of Hamiltonian cycles for arbitrary graphs. By integrating out quadratic fluctuations around the saddle point, one obtains an estimate for the number which reflects characteristics of graphs well. The accuracy of the estimate is verified by applying it to 2d square lattices with various boundary conditions. This is the first example of extracting meaningful information from the quadratic approximation to the field theory representation.

cond-mat.stat-mech↗

arXiv1998

Counting Hamiltonian cycles on planar random lattices

A Hamiltonian cycle of a graph is a closed path which visits each of the vertices once and only once. In this article, Hamiltonian cycles on planar random lattices are considered. The generating function for the number of Hamiltonian cycles is obtained and its singularity is studied. Relation to two-dimensional quantum gravity is discussed.

cond-mat.stat-mech↗

arXiv1995

A connection between lattice and surgery constructions of three-dimensional topological field theories

We study the relation between lattice construction and surgery construction of three-dimensional topological field theories. We show that a class of the Chung-Fukuma-Shapere theory on the lattice has representation theoretic reformulation which is closely related to the Altschuler-Coste theory constructed by surgery. There is a similar relation between the Turaev-Viro theory and the Reshetikhin-Turaev theory.

hep-th↗

arXiv1995

Feynman rules for string field theories with discrete target space

We derive a minimal set of Feynman rules for the loop amplitudes in unitary models of closed strings, whose target space is a simply laced (extended) Dynkin diagram. The string field Feynman graphs are composed of propagators, vertices (including tadpoles) of all topologies, and leg factors for the macroscopic loops. A vertex of given topology factorizes into a fusion coefficient for the matter fields and an intersection number associated with the corresponding punctured surface. As illustration we obtain explicit expressions for the genus-one tadpole and the genus-zero four-loop amplitude.

hep-th↗

arXiv1995

Renormalization group flow in one- and two-matrix models

Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling constants by taking account of reparametrization identities. Despite the nonlinearity of the equation, the location of fixed points and the scaling exponents can be extracted from the equation. They agree with the spectrum of relevant operators in the exact solution. A linearized $β$-function approximates well the global phase structure which includes several nontrivial fixed points. The global renormalization group flow suggests a kind of $c$-theorem in two-dimensional quantum gravity.

hep-th↗

arXiv1994

On three-dimensional topological field theories constructed from $D^ω(G)$ for finite group

We investigate the 3d lattice topological field theories defined by Chung, Fukuma and Shapere. We concentrate on the model defined by taking a deformation $\D{G}$ of the quantum double of a finite commutative group $G$ as the underlying Hopf algebra. It is suggested that Chung-Fukuma-Shapere partition function is related to that of Dijkgraaf-Witten by $\zcfs = |\zdw|^2$ when $G=\Z_{2N+1}$. For $G=\Z_{2N}$, such a relation does not hold.

hep-th↗

arXiv1993

Nonlinear Renormalization Group Equation for Matrix Models

An exact renormalization group equation is derived for the free energy of matrix models. The renormalization group equation turns out to be nonlinear for matrix models, as opposed to linear for vector models. An algorithm for determining the critical coupling constant and the critical exponent is obtained. As concrete examples, one-matrix models with one and two coupling constants are analyzed and the exact values of the critical coupling constant and the associated critical exponent are found.

hep-th↗

arXiv1993

Renormalization Group Approach to Matrix Models and Vector Models

The renormalization group approach is studied for large $N$ models. The approach of Brézin and Zinn-Justin is explained and examined for matrix models. The validity of the approach is clarified by using the vector model as a similar and simpler example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization freedom in field space provides infinitely many identities which reduce the infinite dimensional coupling constant space to that of finite dimensions. The effective beta functions give exact values for the fixed points and the susceptibility exponents. A detailed study of the effective renormalization group flow is presented for cases with up to two coupling constants. We draw the two-dimensional flow diagram.

hep-th↗

arXiv1993

Exact Beta Functions in the Vector Model and Renormalization Group Approach

The validity of the renormalization group approach for large $N$ is clarified by using the vector model as an example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization freedom in field space provides infinitely many identities which reduce the infinite dimensional coupling constant space to that of finite dimensions. The effective beta functions give exact values for the fixed points and the susceptibility exponents.

hep-th↗