Related papers: Thermodynamic geometry of one-dimensional spin one…

We propose the construction of thermodynamic ensembles that minimize the R\'enyi free energy, as an alternative to Gibbs states. For large systems, the local properties of these R\'enyi ensembles coincide with those of thermal equilibrium,…

We investigate the tricritical scaling behavior of the two-dimensional spin-$1$ Blume-Capel model using the Wang-Landau method measuring the joint density of states for lattice sizes up to $48\times 48$ sites. The first-order transition…

Going beyond the classical Gaussian approximation of Einstein's fluctuation theory, Ruppeiner gave it a Riemannian geometric structure with an entropic metric. This yielded a fundamental quantity - the Riemannian curvature, which was used…

A novel geometric formalism for statistical estimation is applied here to the canonical distribution of classical statistical mechanics. In this scheme thermodynamic states, or equivalently, statistical mechanical states, can be…

We study pattern formation within the $J_1$-$J_3$ - spin model on a two-dimensional square lattice in the case of incompatible (ferromagnetic) boundary conditions on the spin field. We derive the discrete-to-continuum $\Gamma$-limit at the…

The new mathematical framework based on the free energy of pure classical fluids presented in [R. D. Rohrmann, Physica A 347, 221 (2005)] is extended to multi-component systems to determine thermodynamic and structural properties of…

We study numerically a two-dimensional version of the Burrige-Knopoff model. We calculate spatial and temporal correlation functions and compare their behavior with the results found for the one-dimensional model. The Gutenberg-Richter law…

The exact statistical-mechanical solution for the equilibrium properties, both thermodynamic and structural, of one-dimensional fluids of particles interacting via the triangle-well and the ramp potentials is worked out. In contrast to…

We formulate correlation functions for a one-dimensional interacting spinless fermion model at finite temperature. By combination of a lattice path integral formulation for thermodynamics with the algebraic Bethe ansatz for fermion systems,…

We consider a formal discretisation of Euclidean quantum gravity defined by a statistical model of random $3$-regular graphs and making using of the Ollivier curvature, a coarse analogue of the Ricci curvature. Numerical analysis shows that…

We use a self-consistent Ornstein-Zernike approximation to study the Blume-Capel ferromagnet on three-dimensional lattices. The correlation functions and the thermodynamics are obtained from the solution of two coupled partial differential…

One-dimensional systems of interacting atoms are an ideal laboratory to study the Kosterlitz-Thouless phase transition. In the renormalization group picture there is essentially a two-parameter phase diagram to explore. We first present how…

In this paper the geometric entanglement (GE) of systems in one spatial dimension (1D) and in the thermodynamic limit is analyzed focusing on two aspects. First, we reexamine the calculation of the GE for translation-invariant matrix…

We study multidimensional gravitational models with scalar curvature nonlinearity of the type 1/R and with form-fields (fluxes) as a matter source. It is assumed that the higher dimensional space-time undergoes Freund-Rubin-like spontaneous…

Expansions through the 24th order at high-temperature and up to 11th order at low-temperature are derived for the main observables of the Blume-Capel model on bipartite lattices (sq, sc and bcc) in 2d and 3d with various values of the spin…

Microscopic models of realistic thermodynamic systems usually involve a number of parameters, not all of equal macroscopic relevance. We examine a decorated $(1+3)$ Ising spin chain containing two microscopic parameters: a "stiff" $K$…

We consider a particular case of the two dimensional Blume-Emery-Griffiths model to study the finite-size scaling for a field driven first-order phase transition with two coexisting phases not related by a symmetry. For low temperatures we…

We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…

We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of…

Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an…