Related papers: Block-diagonalizable two-dimensional generalized I…
We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings,…
Calculating free energy differences is a topic of substantial interest and has many applications including molecular docking and hydration, solvation, and binding free energies which is used in computational drug discovery. However, in…
A mixed basis approach based on density functional theory is extended to one-dimensional(1D) systems. The basis functions here are taken to be the localized B-splines for the two finite non-periodic dimensions and the plane waves for the…
The gain of free energy upon unmixing is determined via application of Markov state modeling (MSM), using an Ising model with a fixed number of up- and down-spins. MSM yields reasonable estimates of the free energies. However, a closer look…
The free energy of the Penner model is shown to be closely related to the integral over the two diagonalizing unitary matrices of a complex rectangular matrix.
We present a self-contained analysis of theories of discrete 2D gravity coupled to matter, using geometric methods to derive equations for generating functions in terms of free (noncommuting) variables. For the class of discrete gravity…
Using the example of the two-dimensional (2D) Ising model, we show that in contrast to what can be done in configuration space, the tensor renormalization group (TRG) formulation allows one to write exact, compact, and manifestly local…
The site-random Ising spin glass model is investigated. We find a rigorous symmetry for the SG correlation and the free energy, which provides some restrictions in the phase diagram. Using the defect energies calculated by the numerical…
In this paper a new approach to solving the Ising-Onsager problem in external magnetic field is investigated. The expression for free energy on one Ising spin in external field both for the twodimensional and threedimensional Ising model…
Using a formalism based on the spectral decomposition of the replicated transfer matrix for disordered Ising models, we obtain several results that apply both to isolated one-dimensional systems and to locally tree-like graph and factor…
We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and…
We study the dynamics of macroscopic observables such as the magnetization and the energy per degree of freedom in Ising spin models on random graphs of finite connectivity, with random bonds and/or heterogeneous degree distributions. To do…
The absolute free energy -- or partition function, equivalently -- of a molecule can be estimated computationally using a suitable reference system. Here, we demonstrate a practical method for staging such calculations by growing a molecule…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
In this paper we present a new approach how to extract polarization-dependent exchange-correlation energy densities for two-dimensional systems from reference densities and energies of quantum dots provided by exact diagonalization.…
In this article we obtain some exact results for the 2D Ising model with a general boundary magnetic field and for a finite size system, by an alternative method to that developed by B. McCoy and T.T. Wu. This method is a generalization of…
This thesis is devoted to ab initio calculations of ground and excited state properties of different systems within density functional theory and time dependent density functional theory. From the numerical point of view we implemented an…
A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…
We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm gives numerically exact results for the…
We propose an algorithm to obtain numerically approximate solutions of the direct Ising problem, that is, to compute the free energy and the equilibrium observables of spin systems with arbitrary two-spin interactions. To this purpose we…