Computer simulation of the critical behavior of magnetic systems with competition between the short- and long-range interactions

We have considered a classical spin system, consisting of 3-component unit vectors, associated with a two-dimensional lattice {uk, k∈ Z2}, and interacting via translationally invariant pair potentials, isotropic in spin space, and of the long-range form [Formula: see text] Here ∊ is a positive constant setting energy and temperature scales (i.e. T*=k B T /∊), P2 denotes the second Legendre polynomial, and xj are dimensionless coordinates of the lattice sites. Available theorems entail the existence of an ordering transition at finite temperature when 0 < σ < 2, and its absence when σ ≥ 2. We have studied the border case σ=2, by means of computer simulation. Similarly to the nearest-neighbour counterpart of the present model, and to other long-range models, we found evidence suggesting a transition to a low-temperature phase with slow decay of correlations and infinite susceptibility, i.e. a Berezhinski[Formula: see text]–Kosterlitz–Thouless-like transition; the transition temperature was estimated to be Θ=1.112 ± 0.005.

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Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

Physical Review E ◽

10.1103/physreve.93.062103 ◽

2016 ◽

Vol 93 (6) ◽

Cited By ~ 4

Author(s):

José A. Carrasco ◽

Federico Finkel ◽

Artemio González-López ◽

Miguel A. Rodríguez ◽

Piergiulio Tempesta

Keyword(s):

Long Range ◽

Critical Behavior ◽

Spin Chains ◽

Long Range Interactions

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COMPUTER SIMULATION STUDY OF A DISORDERED ONE-DIMENSIONAL NEMATOGENIC LATTICE MODEL WITH LONG-RANGE INTERACTIONS ISOTROPIC IN SPIN SPACE

International Journal of Modern Physics B ◽

10.1142/s0217979295001312 ◽

1995 ◽

Vol 09 (25) ◽

pp. 3345-3354 ◽

Cited By ~ 1

Author(s):

S. ROMANO

Keyword(s):

Computer Simulation ◽

Long Range ◽

Temperature Phase ◽

Spin Space ◽

Rigorous Results ◽

One Dimensional ◽

Pair Potentials ◽

Long Range Interactions ◽

Invariant Pair ◽

Ordering Transition

We have considered a classical spin system, consisting of 3-component unit vectors, associated with a one-dimensional lattice {uk, k ∈ Z}, and interacting via translationally invariant pair potentials, isotropic in spin space, and of the long-range form [Formula: see text] where ∊ is a positive constant setting energy and temperature scales (i.e. T* = kBT/∊). Extending previous rigorous results, one can prove the existence of an ordering transition at finite temperature when 0 < σ < 1, and its absence when σ ≥ 1. We have studied the border case σ = 1, by means of computer simulation. Similarly to the magnetic counterparts of the present model, we found evidence suggesting a transition to a low-temperature phase with slow decay of correlations and infinite susceptibility, i.e. a Berezhinskiǐ–Kosterlitz–Thouless-like transition; the transition temperature was estimated to be Θ = 0.475 ± 0.005.

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