Related papers: Transfer matrix in counting problems made easy
Transfer learning is a popular paradigm for utilizing existing knowledge from previous learning tasks to improve the performance of new ones. It has enjoyed numerous empirical successes and inspired a growing number of theoretical studies.…
We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…
We construct two spin models on lattices (both two and three-dimensional) to study the capability of quantum computational power as a function of temperature and the system parameter. There exists a finite region in the phase diagram such…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
This paper proposes a new methodology to maximize the feasible set of power injections and cross-border power transfers in meshed multi-area power systems. The approach used polyhedral computation schemes and is an extension to the classic…
In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite…
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…
We provide a complete thermodynamic solution of a 1D hopping model in the presence of a random potential by obtaining the density of states. Since the partition function is related to the density of states by a Laplace transform, the…
A method is proposed for exactly calculating the partition function of a rectangular Ising lattice with the presence of a uniform external field. This approach is based on the method of the transfer matrix developed about seventy years ago…
One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…
We study a class of statistical systems which simulate 3D gonihedric system on euclidean lattice. We have found the exact partition function of the 3D-model and the corresponding critical indices analysing the transfer matrix…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
While true phase transitions are forbidden in one-dimensional systems with short-range interactions, several models have recently been shown to exhibit sharp yet analytic thermodynamic anomalies that mimic thermal phase transitions. We show…
This article is concerned with a mathematical tool, the Associated Transfer Matrix T, which proves useful in the study of a wide class of physical problems involving multilayer heterostructures. General properties of linear, second order…
Transparent boundary conditions for the time-dependent Schrodinger equation are implemented using the R-matrix method. The employed scattering formalism is suitable for describing open quantum systems and provides the framework for the…
We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal…
We consider integrable quantum spin chains with competing interactions. We apply the quantum transfer matrix approach to these spin chains. This allowed us to derive a set of non-linear integral equations for the thermodynamics of these…
We introduce a numerical tensor-network method to compute the statistics of the charge transferred across an interface partitioning an interacting one-dimensional many-body lattice system with $U(1)$ symmetry. Our approach is based on a…
In this paper, the transfer matrix technique using the $k$-matching vector is developed to compute the number of $k$-matchings in an arbitrary graph which can be constructed by successive amalgamations over sets of cardinality two. This…