• Corpus ID: 230523674

Quantitative disorder effects in low-dimensional spin systems

@inproceedings{Dario2021QuantitativeDE,
  title={Quantitative disorder effects in low-dimensional spin systems},
  author={Paul Dario and Matan Harel and Ron Peled},
  year={2021}
}
The Imry–Ma phenomenon, predicted in 1975 by Imry and Ma and rigorously established in 1989 by Aizenman and Wehr, states that first-order phase transitions of lowdimensional spin systems are ‘rounded’ by the addition of a quenched random field to the quantity undergoing the transition. The phenomenon applies to a wide class of spin systems in dimensions d ≤ 2 and to spin systems possessing a continuous symmetry in dimensions d ≤ 4. This work provides quantitative estimates for the Imry–Ma… 

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References

SHOWING 1-10 OF 59 REFERENCES
Random field induced order in low dimension
We address an unresolved issue in the physics of low-dimensional many-body systems: the question of whether or not a random field can produce order at low temperatures for statistical mechanical
Destruction of long range order in one-dimensional and two-dimensional systems having a continuous symmetry group. I. Classical systems
The low-temperature state of two-dimensional classical systems, which in the three-dimensional case have an ordered phase with a spontaneous violation of a continuous symmetry (magnetic substances,
A Power-Law Upper Bound on the Correlations in the 2D Random Field Ising Model
AbstractAs first asserted by Y. Imry and S-K Ma, the famed discontinuity of the magnetization as function of the magnetic field in the two dimensional Ising model is eliminated, for all temperatures,
DESTRUCTION OF LONG-RANGE ORDER IN ONE-DIMENSIONAL AND TWO-DIMENSIONAL SYSTEMS POSSESSING A CONTINUOUS SYMMETRY GROUP . II . QUANTUM
The asymptotic behavior of the correlations in the low-temperature phase are found for the following two-dimensional quantum systems: a two-dimensional lattice of plane rotators, two-dimensional
Rounding effects of quenched randomness on first-order phase transitions
Frozen-in disorder in an otherwise homogeneous system, is modeled by interaction terms with random coefficients, given by independent random variables with a translation-invariant distribution. For
Theory of the Random Field Ising Model
A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition
Unified picture of ferromagnetism, quasi-long-range order, and criticality in random-field models.
TLDR
The interplay between ferromagnetism, quasi-long-range order (QLRO), and criticality in the d-dimensional random-field O(N) model in the whole (N, d) diagram is studied.
Rounding of first-order phase transitions in systems with quenched disorder.
TLDR
For random-field models, this work rigorously proves uniqueness of the Gibbs state 2D Ising systems, and absence of continuous symmetry breaking in the Heisenberg model in d\ensuremath{\le}4, as predicted by Imry and Ma.
Quasi-long range order in glass states of impure liquid crystals, magnets, and superconductors
We consider glass states of several disordered systems: vortices in impure superconductors, amorphous magnets, and nematic liquid crystals in random porous media. All these systems can be described
Phase transition in the 3d random field Ising model
We show that the three-dimensional Ising model coupled to a small random magnetic field is ordered at low temperatures. This means that the lower critical dimension,dl for the theory isdl≦2, settling
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