Infinite differentiability for one-dimensional spin system with long range random interaction

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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Ergodicity variation in a long range interacting one-dimensional Ising spin system subject to a time-varying magnetic field

Journal of Physics Conference Series ◽

10.1088/1742-6596/1253/1/012009 ◽

2019 ◽

Vol 1253 ◽

pp. 012009

Author(s):

Gehad Sadiek ◽

Habeba Al-mutairi

Keyword(s):

Magnetic Field ◽

Long Range ◽

Spin System ◽

Time Varying ◽

One Dimensional ◽

Ising Spin ◽

Ising Spin System

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Kinetic theory of one-dimensional homogeneous long-range interacting systems with an arbitrary potential of interaction

Physical Review E ◽

10.1103/physreve.102.052110 ◽

2020 ◽

Vol 102 (5) ◽

Author(s):

Jean-Baptiste Fouvry ◽

Pierre-Henri Chavanis ◽

Christophe Pichon

Keyword(s):

Kinetic Theory ◽

Long Range ◽

One Dimensional ◽

Interacting Systems ◽

Arbitrary Potential

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Quasi-1D XY antiferromagnet Sr2Ni(SeO3)2Cl2 at Sakai-Takahashi phase diagram

Scientific Reports ◽

10.1038/s41598-021-94390-3 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

E. S. Kozlyakova ◽

A. V. Moskin ◽

P. S. Berdonosov ◽

V. V. Gapontsev ◽

S. V. Streltsov ◽

...

Keyword(s):

Phase Diagram ◽

Long Range ◽

Density Functional ◽

Uniaxial Anisotropy ◽

Exchange Interactions ◽

Spin Liquid ◽

Functional Theory ◽

One Dimensional ◽

Ordered Phases ◽

Experimental Findings

AbstractUniform quasi-one-dimensional integer spin compounds are of interest as a potential realization of the Haldane conjecture of a gapped spin liquid. This phase, however, has to compete with magnetic anisotropy and long-range ordered phases, the implementation of which depends on the ratio of interchain J′ and intrachain J exchange interactions and both uniaxial D and rhombic E single-ion anisotropies. Strontium nickel selenite chloride, Sr2Ni(SeO3)2Cl2, is a spin-1 chain system which passes through a correlations regime at Tmax ~ 12 K to long-range order at TN = 6 K. Under external magnetic field it experiences the sequence of spin-flop at Bc1 = 9.0 T and spin-flip transitions Bc2 = 23.7 T prior to full saturation at Bsat = 31.0 T. Density functional theory provides values of the main exchange interactions and uniaxial anisotropy which corroborate the experimental findings. The values of J′/J = 0.083 and D/J = 0.357 place this compound into a hitherto unoccupied sector of the Sakai-Takahashi phase diagram.

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