scholarly journals A geometric Monte Carlo algorithm for the antiferromagnetic Ising model with “topological” term at θ=π

2014 ◽  
Vol 883 ◽  
pp. 656-684 ◽  
Author(s):  
V. Azcoiti ◽  
G. Cortese ◽  
E. Follana ◽  
M. Giordano
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Algorithm ◽  
Antiferromagnetic Ising Model ◽  
Topological Term

SPECIAL-PURPOSE ISING MODEL RANDOM LATTICE PROCESSOR

1991 ◽  
Vol 02 (03) ◽  
pp. 805-816 ◽  
Author(s):  
V.B. ANDREICHENKO ◽  
VL.S. DOTSENKO ◽  
L.N. SHCHUR ◽  
A.L. TALAPOV
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Step ◽  
Monte Carlo Algorithm ◽  
Price Ratio ◽  
Random Lattice ◽  
Spin Flip ◽  
Different Types ◽  
Memory Cycle Time ◽  
Memory Cycle

We have designed and built a special purpose processor with a very good performance to price ratio, which permits to propose a new way for parallel computing. A simple one spin flip Monte Carlo algorithm is realized in hardware, so the processor is suitable for studies of dynamic as well as thermodynamic properties of the two-dimensional Ising model with different types of inhomogeneities. The speed of the processor is defined completely by the speed of memories used in it: to perform an elementary Monte Carlo step the processor needs a time only several percent larger than one memory cycle time. So it realizes the fastest possible one spin flip Monte Carlo processor architecture.

scholarly journals Monte Carlo simulation of stoquastic Hamiltonians

2015 ◽  
Vol 15 (13&14) ◽  
pp. 1122-1140
Author(s):  
Sergey Bravyi
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Ground State ◽  
State Energy ◽  
Transverse Field ◽  
Variable Number ◽  
Monte Carlo Algorithm ◽  
Standard Product ◽  
Ferromagnetic Ising Model ◽  
Transverse Field Ising Model

Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field Ising Model (TIM), the Heisenberg model on bipartite graphs, and the bosonic Hubbard model. Here we consider the problem of estimating the ground state energy of a local stoquastic Hamiltonian $H$ with a promise that the ground state of $H$ has a non-negligible correlation with some `guiding' state that admits a concise classical description. A formalized version of this problem called Guided Stoquastic Hamiltonian is shown to be complete for the complexity class $\MA$ (a probabilistic analogue of $\NP$). To prove this result we employ the Projection Monte Carlo algorithm with a variable number of walkers. Secondly, we show that the ground state and thermal equilibrium properties of the ferromagnetic TIM can be simulated in polynomial time on a classical probabilistic computer. This result is based on the approximation algorithm for the classical ferromagnetic Ising model due to Jerrum and Sinclair (1993).

scholarly journals PROPERTIES OF ITERATIVE MONTE CARLO SINGLE HISTOGRAM REWEIGHTING

2005 ◽  
Vol 16 (12) ◽  
pp. 1943-1952 ◽  
Author(s):  
MARTIN GMITRA ◽  
DENIS HORVÁTH
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Ising Model ◽  
Probability Distribution Function ◽  
Stationary Regime ◽  
Simple Relation ◽  
Monte Carlo Algorithm ◽  
Linear Filtering ◽  
Suggested Model ◽  
Temperature Variable

We present an iterative Monte Carlo algorithm for which the temperature variable is attracted by a critical point. The algorithm combines techniques of single histogram reweighting and linear filtering. The ferromagnetic 2D Ising model is studied numerically as an illustration. In that case, the iterations reach a stationary regime with an invariant probability distribution function of temperature which peaked near the pseudocritical temperature of the specific heat. The sequence of generated temperatures is analyzed in terms of stochastic autoregressive model. The error of histogram reweighting can be better understood within the suggested model. The presented model yields a simple relation, connecting the variance of pseudocritical temperature and the parameter of linear filtering.

scholarly journals Приближение Бете для двумерной спин-псевдоспиновой системы

2019 ◽  
Vol 61 (9) ◽  
pp. 1676
Author(s):  
Ю.Д. Панов ◽  
А.С. Москвин ◽  
В.А. Улитко ◽  
А.А. Чиков
Keyword(s):  
Numerical Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Ising Model ◽  
Two Dimensional ◽  
Bethe Approximation ◽  
Nonmagnetic Impurities ◽  
Analytical Results ◽  
Antiferromagnetic Ising Model

A two-dimensional spin-pseudospin model is considered, which generalizes a diluted antiferromagnetic Ising model with charged nonmagnetic impurities in the case of two types of charges. The analytical results in the Bethe approximation are compared with the results of numerical simulation using the classical Monte Carlo method for various parameters.

Sign in / Sign up

Export Citation Format

Share Document