Exact ground states of onedimensional longrange randomfield Ising magnets
Abstract
We investigate the onedimensional longrange randomfield Ising magnet with Gaussian distribution of the random fields. In this model, a ferromagnetic bond between two spins is placed with a probability p ∼r^{1σ}, where r is the distance between these spins and σ is a parameter to control the effective dimension of the model. Exact ground states at zero temperature are calculated for system sizes up to L =2^{19} via graph theoretical algorithms for four different values of σ ∈{0.25,0.4,0.5,1.0} while varying the strength h of the random fields. For each of these values several independent physical observables are calculated, i.e., magnetization, Binder parameter, susceptibility, and a specificheatlike quantity. The ferromagnetparamagnet transitions at critical values h_{c}(σ) as well as the corresponding critical exponents are obtained. The results agree well with theory, and interestingly we find for σ =1/2 the data is compatible with a critical randomfield strength h_{c}>0.
 Publication:

Physical Review B
 Pub Date:
 July 2014
 DOI:
 10.1103/PhysRevB.90.014207
 arXiv:
 arXiv:1307.3987
 Bibcode:
 2014PhRvB..90a4207D
 Keywords:

 05.50.+q;
 64.60.De;
 75.40.Mg;
 75.50.Lk;
 Lattice theory and statistics;
 Statistical mechanics of model systems;
 Numerical simulation studies;
 Spin glasses and other random magnets;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics;
 Physics  Computational Physics
 EPrint:
 12 pages, 15 figures