scholarly journals Generalized motion by mean curvature as a macroscopic limit of stochastic ising models with long range interactions and Glauber dynamics

1995 ◽  
Vol 169 (1) ◽  
pp. 61-97 ◽  
Author(s):  
Markos A. Katsoulakis ◽  
Panagiotis E. Souganidis
Keyword(s):  
Long Range ◽  
Mean Curvature ◽  
Glauber Dynamics ◽  
Ising Models ◽  
Long Range Interactions ◽  
Motion By Mean Curvature

scholarly journals Geometry of contours and Peierls estimates in d=1 Ising models with long range interactions

2005 ◽  
Vol 46 (5) ◽  
pp. 053305 ◽  
Author(s):  
Marzio Cassandro ◽  
Pablo Augusto Ferrari ◽  
Immacolata Merola ◽  
Errico Presutti
Keyword(s):  
Long Range ◽  
Ising Models ◽  
Long Range Interactions ◽  
Peierls Estimates

scholarly journals MONTE-CARLO CALCULATIONS OF PHASE TRANSITION TEMPERATURE IN THE ISING MODEL WITH LONG RANGE INTERACTIONS

2017 ◽  
Vol 21 (6) ◽  
pp. 161-170
Author(s):  
A.A. Biryukov ◽  
Y.V. Degtyarova
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Transition Temperature ◽  
Long Range ◽  
Phase Transition Temperature ◽  
Three Dimensional ◽  
Ising Models ◽  
Monte Carlo Calculations ◽  
Spin Interactions ◽  
Long Range Interactions

The article deals with two-dimensional and three-dimensional Ising models with the long-range spin interactions. The intensity of interaction between the spins relies decreasing with distance r as a power law r-d-σ with dimensional d and parameter σ. The research are conducted by Monte-Carlo method with Metropolis algorithm using parallel computing techniques. On the basis of nu- merical simulation the dependence of the phase transition temperature on the parameter σ is found. It is shown that at phase transition temperature decreases with increasing σ.

scholarly journals Comment on “Many-body localization in Ising models with random long-range interactions”

2017 ◽  
Vol 96 (5) ◽  
Author(s):  
Andrii O. Maksymov ◽  
Noah Rahman ◽  
Eliot Kapit ◽  
Alexander L. Burin
Keyword(s):  
Long Range ◽  
Ising Models ◽  
Many Body ◽  
Long Range Interactions

Phase transitions in long-range Ising models and an optimal condition for factors of -measures

2017 ◽  
Vol 39 (5) ◽  
pp. 1317-1330 ◽  
Author(s):  
ANDERS JOHANSSON ◽  
ANDERS ÖBERG ◽  
MARK POLLICOTT
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Optimal Condition ◽  
Long Range ◽  
Ising Models ◽  
Inverse Temperature ◽  
Shift Space ◽  
Long Range Interactions ◽  
Full Shift ◽  
Block Factor

We weaken the assumption of summable variations in a paper by Verbitskiy [On factors of $g$-measures. Indag. Math. (N.S.)22 (2011), 315–329] to a weaker condition, Berbee’s condition, in order for a one-block factor (a single-site renormalization) of the full shift space on finitely many symbols to have a $g$-measure with a continuous $g$-function. But we also prove by means of a counterexample that this condition is (within constants) optimal. The counterexample is based on the second of our main results, where we prove that there is a critical inverse temperature in a one-sided long-range Ising model which is at most eight times the critical inverse temperature for the (two-sided) Ising model with long-range interactions.

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