Related papers: The Free Energy Formula
In contrast to the infinite chain, the low-temperature expansion of a one-dimensional free-field Ising model has a strong dependence on boundary conditions. I derive explicit formula for the leading term of the expansion both under open and…
We consider a two-dimensional Ising field theory on a space with boundary in the presence of a piecewise constant boundary magnetic field which is allowed to change value discontinuously along the boundary. We assume zero magnetic field in…
The two-dimensional Ising model is representable as a lattice free-fermion field theory in terms of the integral over anticommuting Grassmann variables. The exact solution in a zero magnetic field then follows by evaluating Gaussian…
For the generalized Ising models with all possible interactions within a face of the square lattice the formulas for finding partition function and free energy per lattice site in the thermodynamic limit were derived on a certain, in the…
In this work, we propose a method for calculating the free energy of anisotropic quantum spin systems. We use the Hubbard-Stratonovich transformation to express the partition function of a generic bilinear super-exchange Hamiltonian in…
By quenching into the metastable region of the three-dimensional Ising model, we investigate the paths that the magnetization (energy) takes as a function of time. We accumulate the magnetization (energy) paths into time-dependent…
In [Physical Magazine, 35(3):593-601, 1977], Thouless, Anderson, and Palmer derived a representation for the free energy of the Sherrington-Kirkpatrick model, called the TAP free energy, written as the difference of the energy and entropy…
The authors of [Ann. Henri Poincar\'{e} 16 (2015) 691-708] introduced a multi-species version of the Sherrington-Kirkpatrick model and suggested the analogue of the Parisi formula for the free energy. Using a variant of Guerra's replica…
We present a detailed analysis of the universal relationship between grain boundary (GB) free energy and GB self-diffusion coefficient derived by Borisov et al. (1964). This relationship was expressed by a simple equation that was used in…
We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for $a^2 \rho \ll 1$ and $\beta \rho \gtrsim 1$ the free energy per unit volume differs from the one of the…
We prove Goldschmidt's formula [Phys. Rev. B 47 (1990) 4858] for the free energy of the quantum random energy model. In particular, we verify the location of the first order and the freezing transition in the phase diagram. The proof is…
Bethe Ansatz solutions of the open spin-1/2 integrable XXZ quantum spin chain at roots of unity with nondiagonal boundary terms containing two free boundary parameters have recently been proposed. We use these solutions to compute the…
An ansatz applied to the two-dimensional Ising model in an external magnetic field h gives rise to an exactly soluble model. The singularity in the magnetization found by Onsager does not survive the presence of the external magnetic field…
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…
Sigma models arise frequently in particle physics and condensed-matter physics as low-energy effective theories. In this paper I compute the exact free energy at any temperature in two hierarchies of integrable sigma models in two…
We compute the free energy at all temperatures for the spherical pure $p$-spin models from the generalized Thouless-Anderson-Palmer representation. This is the first example of a mixed $p$-spin model for which the free energy is computed in…
Finite size effect in critical systems can be interpreted as universal Casimir forces. Here we compare the Casimir force for free, periodic and antiperiodic boundary conditions in the exactly calculable case of the Ising model in one and…
The crystalline ferromagnet with dipole-dipole interactions is studied within the framework of the three-dimensional random-field Ising model. The field distribution function and the analytic expression for temperature dependent free energy…
We obtain the diagonal reflection matrices for a recently introduced family of dilute ${\rm A}_L$ lattice models in which the ${\rm A}_3$ model can be viewed as an Ising model in a magnetic field. We calculate the surface free energy from…
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…