Related papers: A Worm Algorithm for Two-Dimensional Spin Glasses
An exact algorithm is used to compute the degeneracies of the excited states of the bimodal Ising spin glass in two dimensions. It is found that the specific heat at arbitrary low temperature is not a self-averaging quantity and has a…
We discuss recently introduced numerical linked-cluster (NLC) algorithms that allow one to obtain temperature-dependent properties of quantum lattice models, in the thermodynamic limit, from exact diagonalization of finite clusters. We…
The frustrated Ising model in two dimensions is revisited. The frustration is quantified in terms of the number of non-trivial plaquettes which is invariant under the Nishimori gauge symmetry. The exact ground state energy is calculated…
We study finite-temperature properties of strongly correlated fermions in two-dimensional optical lattices by means of numerical linked cluster expansions, a computational technique that allows one to obtain exact results in the…
The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing…
It is believed that the $\pm J$ Ising spin-glass does not order at finite temperatures in dimension $d=2$. However, using a graphical representation and a contour argument, we prove rigorously the existence of a finite-temperature phase…
The problem of N interacting spins on a lattice is equivalent to one of N clusters linked in a specific manner. The energy of any configuration of spins can be expressed in terms of the energy levels of this cluster. A new expression is…
We establish a polynomial-time approximation algorithm for partition functions of quantum spin models at high temperature. Our algorithm is based on the quantum cluster expansion of Neto\v{c}n\'y and Redig and the cluster expansion approach…
After briefly describing the present status of the spin glass theory, we present a conjecture on the exact location of the multicritical point in the phase diagram of finite-dimensional spin glasses. The theory enables us to understand in a…
A new approach to combinatorial optimization based on systematic move-class deflation is proposed. The algorithm combines heuristics of genetic algorithms and simulated annealing, and is mainly entropy-driven. It is tested on two problems…
We design spin filters for particles with potentially arbitrary spin S (= 1/2, 1, 3/2,....) using a one-dimensional periodic chain of magnetic atoms as a quantum device. Describing the system within a tight-binding formalism we present an…
We perform Monte Carlo simulations of large two-dimensional Gaussian Ising spin glasses down to very low temperatures $\beta=1/T=50$. Equilibration is ensured by using a cluster algorithm including Monte Carlo moves consisting of flipping…
The loop gas approach to lattice field theory provides an alternative, geometrical description in terms of fluctuating loops. Statistical ensembles of random loops can be efficiently generated by Monte Carlo simulations using the worm…
We compute the exact partition function of 2d Ising spin glasses with binary couplings. In these systems, the ground state is highly degenerate and is separated from the first excited state by a gap of size 4J. Nevertheless, we find that…
Standard Monte Carlo cluster algorithms have proven to be very effective for many different spin models, however they fail for frustrated spin systems. Recently a generalized cluster algorithm was introduced that works extremely well for…
We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…
We use the complex $\phi^4$ field at finite density as a model system for developing further techniques based on worldline formulations of lattice field theories. More specifically we: 1) Discuss new variants of the worm algorithm for…
We study link-diluted $\pm J$ Ising spin glass models on the hierarchical lattice and on a three-dimensional lattice close to the percolation threshold. We show that previously computed zero temperature fixed points are unstable with…
We have developed a new method for evaluating the specific heat of lattice spin systems. It is based on the knowledge of high-temperature series expansions, the total entropy of the system and the low-temperature expected behavior of the…
We introduce a generalized worldline model where the partition function is a sum over configurations of a conserved flux on a d-dimensional lattice. The weights for the configurations of the corresponding worldlines have factors living on…