scholarly journals Critical Behavior of Classical Spin Models and Local Cohomology

2007 ◽  
pp. 279-290
Author(s):  
A. Patrascioiu ◽  
E. Seiler
Keyword(s):  
Critical Behavior ◽  
Local Cohomology ◽  
Spin Models ◽  
Classical Spin ◽  
Classical Spin Models

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

scholarly journals Completeness of classical spin models and universal quantum computation

2009 ◽  
Vol 2009 (07) ◽  
pp. P07001 ◽  
Author(s):  
Gemma De las Cuevas ◽  
Wolfgang Dür ◽  
Maarten Van den Nest ◽  
Hans J Briegel
Keyword(s):  
Quantum Computation ◽  
Spin Models ◽  
Classical Spin ◽  
Universal Quantum ◽  
Classical Spin Models

scholarly journals Rapid mixing of path integral Monte Carlo for 1D stoquastic Hamiltonians

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 395
Author(s):  
Elizabeth Crosson ◽  
Aram W. Harrow
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Path Integral ◽  
Equilibrium Distribution ◽  
Mixing Time ◽  
Gibbs Distribution ◽  
Convergence Time ◽  
Spin Models ◽  
Classical Spin ◽  
Classical Spin Models

Path integral quantum Monte Carlo (PIMC) is a method for estimating thermal equilibrium properties of stoquastic quantum spin systems by sampling from a classical Gibbs distribution using Markov chain Monte Carlo. The PIMC method has been widely used to study the physics of materials and for simulated quantum annealing, but these successful applications are rarely accompanied by formal proofs that the Markov chains underlying PIMC rapidly converge to the desired equilibrium distribution. In this work we analyze the mixing time of PIMC for 1D stoquastic Hamiltonians, including disordered transverse Ising models (TIM) with long-range algebraically decaying interactions as well as disordered XY spin chains with nearest-neighbor interactions. By bounding the convergence time to the equilibrium distribution we rigorously justify the use of PIMC to approximate partition functions and expectations of observables for these models at inverse temperatures that scale at most logarithmically with the number of qubits. The mixing time analysis is based on the canonical paths method applied to the single-site Metropolis Markov chain for the Gibbs distribution of 2D classical spin models with couplings related to the interactions in the quantum Hamiltonian. Since the system has strongly nonisotropic couplings that grow with system size, it does not fall into the known cases where 2D classical spin models are known to mix rapidly.

scholarly journals Unifying All Classical Spin Models in a Lattice Gauge Theory

2009 ◽  
Vol 102 (23) ◽  
Author(s):  
G. De las Cuevas ◽  
W. Dür ◽  
H. J. Briegel ◽  
M. A. Martin-Delgado
Keyword(s):  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Spin Models ◽  
Classical Spin ◽  
Lattice Gauge ◽  
Classical Spin Models

Inequalities between different classical spin models

1976 ◽  
Vol 57 (5) ◽  
pp. 411-413 ◽  
Author(s):  
J. Bricmont
Keyword(s):  
Spin Models ◽  
Classical Spin ◽  
Classical Spin Models

Classical Magnetism and an Integral Formula Involving Modified Bessel Functions

2018 ◽  
Vol 19 (3-4) ◽  
pp. 409-414 ◽  
Author(s):  
Orion Ciftja
Keyword(s):  
Bessel Functions ◽  
Integral Formula ◽  
Linear Integral Equation ◽  
Matrix Formalism ◽  
Modified Bessel Functions ◽  
Case Scenario ◽  
Spin Models ◽  
Classical Spin ◽  
Linear Integral ◽  
Classical Spin Models

AbstractWe study an integral expression that is encountered in some classical spin models of magnetism. The idea is to calculate the key integral that represents the building block for the expression of the partition function of these models. The general calculation allows one to have a better look at the internal structure of the quantity of interest which, in turn, may lead to potentially new useful insights. We find out that application of two different approaches to solve the problem in a general-case scenario leads to an interesting integral formula involving modified Bessel functions of the first kind which appears to be new. We performed Monte Carlo simulations to verify the correctness of the integral formula obtained. Additional numerical integration tests lead to the same result as well. The approach under consideration, when generalized, leads to a linear integral equation that might be of interest to numerical studies of classical spin models of magnetism that rely on the well-established transfer-matrix formalism.

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