Critical Exponent of the Random Field Hierarchical Model

We study the one dimensional Dyson hierarchical model in presence of a random field. This is a long range model where the interaction scales with the distance in a power law-like form, J(r) ∼ r−ρ, and we can explore mean field and non-mean field behavior by changing ρ. We analyze the model at T = 0 and we numerically compute the non-mean field critical exponents for Gaussian disorder. We also compute an analytic expression for the critical exponent δ, and give an interesting relation between the critical exponents of the disordered model and the ones of the pure model, that seems to break down in the non-mean field region. We finally compare our results for the critical exponents with the expected ones in D-dimensional SR models and with the ones of the straightforward one dimensional long range model

Calcolo degli indici critici del modello gerarchico e considerazioni sugli esponenti critici dei modelli con interazione a corta portata in D dimensioni nello studio di modelli disordinati con campo aleatorio in dimensioni basse. ()