Scaling Function for Equation of State: Weakly Random System in the Limit n->

Kentaro Yamamoto, R. Abe

Critical behavior of weakly random system with a specific impurity correlation is studied by means of 1/ n expansion. The correlation function and the equation of state are derived up to order a2 (a being a measure of randomness) in the limit n →∞. Critical exponents η, β and γ are calculated up to this order. It is shown that these exponents are nonuniversal but satisfy a scaling law relation.

Marek Cieplak, Jayanth R. Banavar

Thomas Chen, Itaru Sasaki

Abstract. In this note, we discuss some basic aspects of the dynamics of a homogenous Fermi gas in a weak random potential, under simplifying assumptions on the particle pair interactions. We are particularly interested in studying the delocalizing effects due to the Pauli principle. We derive the kinetic hydrodynamic limit, determined by a linear Boltzmann equation, for the momentum distribution function. Moreover, we prove that if the initial state is quasifree, then the time evolved state averaged over the randomness, which is by itself not quasifree, has a quasifree hydrodynamic limit. We show that the momentum distributions determined by the Gibbs states of a free fermion field persist into the diffusive time scale; this includes the limit of zero temperature. 1.

Xin Zhang, Gaoke Hu, Yongwen Zhang +2 more

E. Cami, Pere Seglar

Daniel S. Fisher

A real-space renormalization-group treatment of random transverse-field Ising spin chains that was introduced previously is developed and extensively analyzed. It yields results that are asymptotically exact in the critical region near the zero-temperature para-to-ferromagnetic quantum phase transition. In particular, the exact scaling function is obtained for the magnetization as a function of a uniform applied magnetic field and the distance to the critical point, and up to the solution of a linear ordinary differential equation whose solution can be exhaustively analyzed, the scaling function of the average spin-spin correlation function is also obtained. Thus more exact information is obtainable about the critical behavior for this random model than is known for the pure version which is equivalent to the two-dimensional Ising model. The basic reason for this is the extremely broad distribution of energy scales that occurs at low energies near the critical point of the random system. For the random chain the distribution of the magnetization of the first spin in a semi-infinite system is also studied and the results found to agree in the scaling limit with results of McCoy obtained from the exact solution of the closely related McCoy-Wu Ising model; this provides strong justification for the validity of the present approach. The singular properties of the weakly ordered and weakly disordered ``Griffiths' phases'' that occur at zero temperature near the critical point are also studied, as well as the behavior at low but nonzero temperature. Possible extensions of the results and general lessons drawn from them for other random systems are briefly discussed.