Large deviations for the 2D ising model: A lower bound without cluster expansions

1994 ◽  
Vol 74 (1-2) ◽  
pp. 411-432 ◽  
Author(s):  
Dmitry Ioffe
Keyword(s):  
Ising Model ◽  
Lower Bound ◽  
Large Deviations ◽  
Cluster Expansions

Lower bound approximation to the free energy of an Ising model on a simple cubic lattice

1981 ◽  
Vol 59 (10) ◽  
pp. 1291-1295 ◽  
Author(s):  
Chin-Kun Hu ◽  
Wen-Den Chen ◽  
Yu-Ming Shih ◽  
Dong-Chung Jou ◽  
C. K. Pan ◽  
...  
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Lower Bound ◽  
Variational Method ◽  
Critical Point ◽  
Zero Field ◽  
Free Energies ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

We apply a modified Kadanoff's variational method to calculate the lower bound zero-field free energies and their derivatives for an Ising model on the simple cubic lattice. We find a critical point at Kc = 0.2393769 with precision ±10−7.

scholarly journals Large deviations for acyclic networks of queues with correlated Gaussian inputs

2021 ◽  
Author(s):  
Martin Zubeldia ◽  
Michel Mandjes
Keyword(s):  
Lower Bound ◽  
Large Deviations ◽  
Decay Rate ◽  
Exponential Decay ◽  
Gaussian Processes ◽  
Sample Path ◽  
Decay Rates ◽  
Single Server ◽  
Exponential Decay Rate ◽  
Overflow Probability

AbstractWe consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i.d. Gaussian processes with stationary increments and positive drifts, which can be correlated across different queues. The flow of work departing from each server is split deterministically and routed to its neighbors according to a fixed routing matrix, with a fraction of it leaving the network altogether. We study the exponential decay rate of the probability that the steady-state queue length at any given node in the network is above any fixed threshold, also referred to as the ‘overflow probability’. In particular, we first leverage Schilder’s sample-path large deviations theorem to obtain a general lower bound for the limit of this exponential decay rate, as the number of Gaussian processes goes to infinity. Then, we show that this lower bound is tight under additional technical conditions. Finally, we show that if the input processes to the different queues are nonnegatively correlated, non-short-range dependent fractional Brownian motions, and if the processing rates are large enough, then the asymptotic exponential decay rates of the queues coincide with the ones of isolated queues with appropriate Gaussian inputs.

scholarly journals Large deviations and continuum limit in the 2D Ising model

1997 ◽  
Vol 109 (4) ◽  
pp. 435-506 ◽  
Author(s):  
C.-E. Pfister ◽  
Y. Velenik
Keyword(s):  
Ising Model ◽  
Large Deviations ◽  
Continuum Limit

SUPERCRITICAL ISING MODEL ON THE LATTICE FRACTAL — THE SIERPINSKI CARPET

2006 ◽  
Vol 20 (08) ◽  
pp. 409-414 ◽  
Author(s):  
JUN WANG
Keyword(s):  
Boundary Condition ◽  
Ising Model ◽  
Lower Bound ◽  
External Field ◽  
Spectral Gap ◽  
Supercritical Condition ◽  
Sierpinski Carpet ◽  
Fractal Lattice ◽  
Sierpiński Carpet

The spectral gap of the Ising model on the lattice fractal (lattice Sierpinski carpet) with the plus boundary condition is considered. In the absence of an external field and at the supercritical condition, we show a lower bound of the spectral gap of the Ising model.

Cluster expansions in the (2+1)D Ising model

1984 ◽  
Vol 17 (8) ◽  
pp. 1649-1664 ◽  
Author(s):  
C J Hamer ◽  
A C Irving
Keyword(s):  
Ising Model ◽  
Cluster Expansions
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