# 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…

## 2 Citations

Long range order for random field Ising and Potts models

- Physics
- 2021

We present a new and simple proof for the classic results of Imbrie (1985) and Bricmont– Kupiainen (1988) that for the random field Ising model in dimension three and above there is long range order…

Random-field random surfaces

- Mathematics
- 2021

We study how the typical gradient and typical height of a random surface are modified by the addition of quenched disorder in the form of a random independent external field. The results provide…

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