Infinitedisorder critical points of models with stretched exponential interactions
Abstract
We show that an interaction decaying as a stretched exponential function of distance, J(l)∼ e^{cl^a} , is able to alter the universality class of shortrange systems having an infinitedisorder critical point. To do so, we study the lowenergy properties of the random transversefield Ising chain with the above form of interaction by a strongdisorder renormalization group (SDRG) approach. We find that the critical behavior of the model is controlled by infinitedisorder fixed points different from those of the shortrange model if 0 < a < 1/2. In this range, the critical exponents calculated analytically by a simplified SDRG scheme are found to vary with a, while, for a > 1/2, the model belongs to the same universality class as its shortrange variant. The entanglement entropy of a block of size L increases logarithmically with L at the critical point but, unlike the shortrange model, the prefactor is dependent on disorder in the range 0 < a < 1/2. Numerical results obtained by an improved SDRG scheme are found to be in agreement with the analytical predictions. The same fixed points are expected to describe the critical behavior of, among others, the random contact process with stretched exponentially decaying activation rates.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 September 2014
 DOI:
 10.1088/17425468/2014/09/P09027
 arXiv:
 arXiv:1406.3200
 Bibcode:
 2014JSMTE..09..027J
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics
 EPrint:
 16 pages, 3 figures