Related papers: Random Matrix Theory and Classical Statistical Mec…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
We have proposed an efficient algorithm to calculate physical quantities in the translational invariant three-dimensional tensor networks, which is particularly relevant to the study of the three-dimensional classical statistical models and…
We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution…
We consider a two-spin model, represented classically by a nonlinear autonomous Hamiltonian system with two degrees of freedom and a nontrivial integrability condition, and quantum mechanically by a real symmetric Hamiltonian matrix with…
The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…
The critical behavior at a corner in two-dimensional Ising and three-state Potts models is studied numerically on the square lattice using transfer operator techniques. The local critical exponents for the magnetization and the energy…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
We study the matrix ansatz in the quantum group framework, applying integrable systems techniques to statistical physics models. We start by reviewing the two approaches, and then show how one can use the former to get new insight on the…
Critical site percolation on the triangular lattice is described by the Yang-Baxter solvable dilute $A_2^{(2)}$ loop model with crossing parameter specialized to $\lambda=\frac\pi3$, corresponding to the contractible loop fugacity…
After briefly describing the present status of the spin glass theory, we present a conjecture on the exact location of the multicritical point in the phase diagram of finite-dimensional spin glasses. The theory enables us to understand in a…
We consider the 2D critical Ising model with spatially periodic boundary conditions. It is shown that for a suitable reparametrization of the known Boltzmann weights the transfer matrix becomes a polynomial in the variable $\csc(4u)$, being…
We address the geometrical critical behavior of the two-dimensional Q-state Potts model in terms of the spin clusters (i.e., connected domains where the spin takes a constant value). These clusters are different from the usual…
In the first part, we introduce the notion of fractional statistics in the sense of Haldane. We illustrate it on simple models related to anyon physics and to integrable models solvable by the Bethe ansatz. In the second part, we describe…
Visibility graphs are spatial interpretations of time series. When derived from the time evolution of physical systems, the graphs associated with such series may exhibit properties that can reflect aspects such as ergodicity, criticality,…
The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of…
In recent years scale invariant scattering theory provided the first exact access to the magnetic critical properties of two-dimensional statistical systems with quenched disorder. We show how the theory extends to the overlap variables…
We consider quantum quenches in the integrable $SU(3)$-invariant spin chain (Lai-Sutherland model), and focus on the family of integrable initial states. By means of a Quantum Transfer Matrix approach, these can be related to…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…