Related papers: Block-diagonalizable two-dimensional generalized I…
Accurate treatment of the electronic correlation in inhomogeneous electronic systems, combined with the ability to capture the correlation energy of the homogeneous electron gas, allows to reach high predictive power in the application of…
We study the spin-$1/2$ Ising chain with multispin interactions $K$ involving the product of $m$ successive spins, for general values of $m$. Using a change of spin variables the zero-field partition function of a finite chain is obtained…
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…
A generalization of the free energy perturbation identity is derived, and a computational strategy based on this result is presented. A simple example illustrates the efficiency gains that can be achieved with this method.
Dynamical Ising machines achieve accelerated solving of complex combinatorial optimization problems by remapping the convergence to the ground state of the classical spin networks to the evolution of specially constructed continuous…
We study the analytic properties of the scaling function associated with the 2D Ising model free energy in the critical domain $T \to T_c$, $H \to 0$. The analysis is based on numerical data obtained through the Truncated Free Fermion Space…
The intrinsic energy minimization in dynamical systems offers a valuable tool for minimizing the objective functions of computationally challenging problems in combinatorial optimization. However, most prior works have focused on mapping…
We consider the formal reduction of a system of linear differential equations and show that, if the system can be block-diagonalised through transformation with a ramified Shearing-transformation and following application of the Splitting…
The partition function of the 2D Ising model coupled to an external magnetic field is studied. We show that the sum over the spin variables can be reduced to an integration over a finite number of variables. This integration must be…
We consider the Ising spin system, which stems out from the corresponding Multiple-spin exchange (MSE) Hamiltonian, on the special one--dimensional lattice, diamond-plaquette chain. Using the technique e of transfer-matrix we obtain the…
Taking advantage of the advances in generative deep learning, particularly normalizing flow, a framework, called Boltzmann Generator, has recently been proposed for the purpose of generating equilibrium atomic configurations from the…
We study the finite-size scaling of the free energy of the Ising model on lattices with the topology of the tetrahedron and the octahedron. Our construction allows to perform changes in the length scale of the model without altering the…
The exact energy spectrum is developed for a two temperature kinetic Ising spin chain, and its dual reaction diffusion system with spatially alternating pair annihilation and creation rates. Symmetries of the system pseudo-Hamiltonian that…
A soft particle model for diblock (AB) copolymer melts is proposed. Each molecule is mapped onto two soft spheres built by Gaussian A- and B-monomer distributions. An approximate analytical expression for the joint distribution function for…
A two-dimensional bistable lattice is a periodic triangular network of non-linear bi-stable rods. The energy of each rod is piecewise quadratic and has two minima. Consequently, a rod undergoes a reversible phase transition when its…
An efficient Monte Carlo method is extended to evaluate directly domain-wall free-energy for randomly frustrated spin systems. Using the method, critical phenomena of spin-glass phase transition is investigated in 4d +/-J Ising model under…
In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact…
We compute the high-dimensional limit of the free energy associated with a multi-layer generalized linear model. Under certain technical assumptions, we identify the limit in terms of a variational formula. The approach is to first show…
We derive the exact ground-state energy of the one-dimensional Ising model in random fields taking values h, 0 and -h with general probabilities. The random-field Ising model on a ladder is also analyzed by showing its equivalence to the…
The bond-propagation (BP) algorithm for the specific heat of the two dimensional Ising model is developed and that for the internal energy is completed. Using these algorithms, we study the critical internal energy and specific heat of the…