Related papers: Random Matrix Theory and Classical Statistical Mec…
We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields. The spectral problem for this model can be formulated in terms of functional equations obtained by separation of…
Random unimodular lattice triangulations have been recently used as an embedded random graph model, which exhibit a crossover behaviour between an ordered, large-world and a disordered, small-world behaviour. Using the ergodic Pachner flips…
The primary aim of this thesis is to investigate metrics which are induced by a differential form and arise as a critical point of Hitchin's variational principle. Firstly, we investigate metrics associated with the structure group PSU(3)…
The leading irrelevant perturbation, which controls the deviation of critical square lattice Ising model with periodic boundary conditions from its continuous CFT analog is identified. An explicit expression for the coupling constant in…
The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…
In the past 30 years there have been extensive discoveries in the theory of integrable statistical mechanical models including the discovery of non-linear differential equations for Ising model correlation functions, the theory of random…
We introduce varying spin strengths to the Ising model, a central pillar of statistical physics. With inhomogeneous physical systems in mind, but also anticipating interdisciplinary applications, we present the model on network structures…
We establish a symmetry in a variety of integrable stochastic systems: Certain multi-point distributions of natural observables are unchanged under a shift of a subset of observation points. The property holds for stochastic vertex models,…
Statistical mechanics describes interaction between particles of a physical system. Particle properties of the system can be modelled with a random field on a lattice and studied at different distance scales using renormalization group…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
In this paper, firstly we show that the entropy constants of the number of independent sets on certain plane lattices are the same as the entropy constants of the corresponding cylindrical and toroidal lattices. Secondly, we consider three…
We introduce a transfer matrix formalism for the (annealed) Ising model coupled to two-dimensional causal dynamical triangulations. Using the Krein-Rutman theory of positivity preserving operators we study several properties of the emerging…
We study the effect of presence of different types of critical points such as ordinary critical point, multicritical point and quasicritical point along different paths on the Fidelity susceptibility and Loschmidt echo of a three spin…
Machine-learning (ML) models trained on Ising spin configurations have demonstrated surprising effectiveness in classifying phases of Potts models, even when processing severely reduced representations that retain only two spin states. To…
Using variational density matrix optimization with two- and three-index conditions we study the one-dimensional Hubbard model with periodic boundary conditions at various filling factors. Special attention is directed to the full…
This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
We investigate the physical properties of an integrable extension of the Hubbard model with a free parameter $\gamma$ related to the quantum deformation of the superalgebra $sl(2|2)^{(2)}$. The Bethe ansatz solution is used to determine the…