Abstract
We study the one-dimensional Dyson hierarchical model in the presence of a random field. This is a long range model where the interaction scales with the distance in a power-law-like form, , and we can explore mean-field and non-mean-field behavior by changing . We analyze the model at and we numerically compute the non-mean-field critical exponents for Gaussian disorder. We also compute an analytic expression for the critical exponent , and give an interesting relation between the critical exponents of the disordered model and the ones of the pure model, which seems to break down in the non-mean-field region. We finally compare our results for the critical exponents with the expected ones in -dimensional short range models and with the ones of the straightforward one-dimensional long range model.
- Received 15 February 2014
- Revised 26 June 2014
DOI:https://doi.org/10.1103/PhysRevB.90.024203
©2014 American Physical Society