Low-energy fixed points of random Heisenberg models

Low-energy fixed points of random Heisenberg models

The effect of quenched disorder on the low-energy and low-temperature properties of various twoand three-dimensional Heisenberg models is studied by a numerical strong disorder renormalization-group method. For strong enough disorder we have identified two relevant fixed points, in which the gap exponent, v , describing the low-energy tail of the gap distribution P(D);D is independent of disord...

Common random fixed points of compatible random operators

The study of random fixed point theory was initiated by the Prague school of probabilists in the 1950s [12, 13, 26]. Random fixed point theorems are stochastic generalization of classical fixed point theorems. The survey article by Bharucha-Reid [10] attracted the attention of several mathematicians and gave wings to this theory. Itoh [16] extended Spacek’s and Hans’s theorem to multivalued con...

Low Energy Properties of the Random Spin-1/2 Ferromagnetic-Antiferromagnetic Heisenberg Chain

The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet ph...

Approximating fixed points of generalized nonexpansive mappings

Random Fixed Points in a Stochastic Solow Growth Model

This paper presents a complete analysis of a stochastic version of the Solow growth model in which all parameters are ergodic random variables. Applying random dynamical systems theory, we prove that the dynamics and, in particular, the long-run behavior is uniquely determined by a globally attracting stable random xed point. We also discuss the relation of our approach to that of ergodic Marko...