Related papers: Finite size corrections to disordered Ising models…
We analytically derive, in the context of the replica formalism, the first finite size corrections to the average optimal cost in the random assignment problem for a quite generic distribution law for the costs. We show that, when moving…
We investigate the effects of finite size corrections on the overlap probabilities in the Generalized Random Energy Model (GREM) in two situations where replica symmetry is broken in the thermodynamic limit. Our calculations do not use…
We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the "cavity" prediction for…
In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced by a modified hyperscaling relation. As a result, standard…
We study the fixed-magnetization ferromagnetic Ising model on random $d$-regular graphs for $d\ge 3$ and inverse temperature below the tree reconstruction threshold. Our main result is that for each magnetization $\eta$, the free energy…
An analysis is made of various methods of phenomenological renormalization based on finite-size scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made…
Finite size corrections to the pressure (free energy) of the Ising model on a 2 dimensional cylinder are calculated and shown to be consistent with the predictions of conformal field theory. The exact solution of the model is expressed in…
We study a ferromagnetic Ising model on random graphs with a power-law degree distribution and compute the thermodynamic limit of the pressure when the mean degree is finite (degree exponent $\tau>2$), for which the random graph has a…
We compute the finite-size corrections to the free energy, internal energy and specific heat of the critical two-dimensional spin-1/2 Ising model on a triangular and hexagonal lattices wrapped on a torus. We find the general form of the…
We introduce an adaptive-weighted tree tensor network, for the study of disordered and inhomogeneous quantum many-body systems. This ansatz is assembled on the basis of the random couplings of the physical system with a procedure that…
Quite recently, Izmailian and Hu [Phys. Rev. Lett. 86, 5160 (2001)] studied the finite-size correction terms for the free energy per spin and the inverse correlation length of the critical two-dimensional Ising model. They obtained the…
We discuss the origin of the finite size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random phase approximation at long wave lengths. The correction comes from…
Systems with many interacting stochastic constituents are fully characterized by their free energy. Computing this quantity is therefore the objective of various approaches, notably perturbative expansions, which are applied in problems…
We discuss finite-size effects in one disordered ${\lambda}{\phi}^{4}$ model defined in a $d$-dimensional Euclidean space. We consider that the scalar field satisfies periodic boundary conditions in one dimension and it is coupled with a…
We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the important statistical content of such models is given by the normalization constant of the models, and in particular, an…
Using the mapping of the partition function of the two-dimensional Ising model onto a pfaffian we evaluate the domain wall free energy difference for the pure and disordered Ising model close to the pure fixed point. Using this method very…
We present the finite-size scaling theory of one-dimensional quantum critical systems in the presence of boundaries. While the finite-size spectrum in the conformal limit, namely of a conformal field theory with conformally invariant…
The equation of state of the universality class of the 3D Ising model is determined numerically in the critical domain from quantum field theory and renormalization group techniques. The starting point is the five loop perturbative…
We derive exact finite-size corrections for the free energy $F$ of the Ising model on the ${\cal M} \times 2 {\cal N}$ square lattice with Brascamp-Kunz boundary conditions. We calculate ratios $r_p(\rho)$ of $p$th coefficients of F for the…
A previously introduced real space renormalization-group treatment of the random transverse-field Ising spin chain is extended to provide detailed information on the distribution of the energy gap and the end-to-end correlation function for…