On the absence of breakdown of symmetry for the plane rotator model with long-range random interaction

1983 ◽  
Vol 32 (3) ◽  
pp. 627-648 ◽  
Author(s):  
P. Picco
Keyword(s):  
Long Range ◽  
Rotator Model ◽  
Random Interaction ◽  
Plane Rotator

Dynamical Plane Rotator Model. III

1982 ◽  
Vol 51 (2) ◽  
pp. 390-396 ◽  
Author(s):  
Minoru Takahashi
Keyword(s):  
Rotator Model ◽  
Dynamical Plane ◽  
Plane Rotator

scholarly journals Monte Carlo Simulation and Static and Dynamic Critical Behavior of the Plane Rotator Model

1978 ◽  
Vol 60 (6) ◽  
pp. 1669-1685 ◽  
Author(s):  
S. Miyashita ◽  
H. Nishimori ◽  
A. Kuroda ◽  
M. Suzuki
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Critical Behavior ◽  
Rotator Model ◽  
Plane Rotator

Transfer matrix in plane-rotator model

1984 ◽  
Vol 104 (6-7) ◽  
pp. 357-360 ◽  
Author(s):  
Daniel C. Mattis
Keyword(s):  
Transfer Matrix ◽  
Rotator Model ◽  
Plane Rotator

scholarly journals Quantum Hopfield Model

Physics ◽  
2020 ◽  
Vol 2 (2) ◽  
pp. 184-196 ◽  
Author(s):  
Masha Shcherbina ◽  
Brunello Tirozzi ◽  
Camillo Tassi
Keyword(s):  
Free Energy ◽  
Long Range ◽  
Thermodynamic Limit ◽  
Random Variables ◽  
Hopfield Model ◽  
Xy Model ◽  
One Dimensional ◽  
Random Interaction ◽  
Independent Identically Distributed

We find the free-energy in the thermodynamic limit of a one-dimensional XY model associated to a system of N qubits. The coupling among the σ i z is a long range two-body random interaction. The randomness in the couplings is the typical interaction of the Hopfield model with p patterns ( p < N ), where the patterns are p sequences of N independent identically distributed random variables (i.i.d.r.v.), assuming values ± 1 with probability 1 / 2 . We show also that in the case p ≤ α N , α ≠ 0 , the free-energy is asymptotically independent from the choice of the patterns, i.e., it is self-averaging.

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