scholarly journals Classical spin models with broken symmetry: Random-field-induced order and persistence of spontaneous magnetization in the presence of a random field

2014 ◽  
Vol 90 (17) ◽  
Author(s):  
Anindita Bera ◽  
Debraj Rakshit ◽  
Maciej Lewenstein ◽  
Aditi Sen(De) ◽  
Ujjwal Sen ◽  
...  
Keyword(s):  
Random Field ◽  
Spontaneous Magnetization ◽  
Broken Symmetry ◽  
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 Average properties of combinatorial problems and thermodynamics of spin models on graphs

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Alessandro Vezzani ◽  
Davide Cassi ◽  
Raffaella Burioni
Keyword(s):  
Random Walks ◽  
Spontaneous Magnetization ◽  
Discrete Symmetry ◽  
Combinatorial Problems ◽  
Infinite Graphs ◽  
Continuous Symmetry ◽  
Spin Models ◽  
Graph Topology ◽  
International Audience ◽  
Classical Spin Models

International audience The study of thermodynamic properties of classical spin models on infinite graphs naturally leads to consider the new combinatorial problems of random-walks and percolation on the average. Indeed, spinmodels with O(n) continuous symmetry present spontaneous magnetization only on transient on the average graphs, while models with discrete symmetry (Ising and Potts) are spontaneously magnetized on graphs exhibiting percolation on the average. In this paper we define the combinatorial problems on the average, showing that they give rise to classifications of graph topology which are different from the ones obtained in usual (local) random-walks and percolation. Furthermore, we illustrate the theorem proving the correspondence between Potts model and average percolation.

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
Sign in / Sign up

Export Citation Format

Share Document