J. Fernando Perez

Long Range Order in the Ground State of Two-Dimensional Antiferromagnets

Abstract We show the existence of long range order in the ground state of the two-dimensional isotropic Heisenberg antiferromagnet for S⩾ 3 2 . The method yields also long range order in the ground state for the larger class of anisotropic quantum antiferromagnetic spin systems with or without transverse magnetic fields.

Generalized point interactions in one-dimensional quantum mechanics

There is a four-parameter family of point interactions in one-dimensional quantum mechanics. They represent all possible self-adjoint extensions of the kinetic energy operator. If time-reversal invariance is imposed, the number of parameters is reduced to three. One of these point interactions is the familiar function potential but the other generalized ones do not seem to be widely known. We present a pedestrian approach to this subject and comment on a recent controversy in the literature concerning the so-called interaction. We emphasize that there is little resemblance between the interaction and what its name suggests.

Stability theory for solitary-wave solutions of scalar field equations

We prove stability and instability theorems for solitary-wave solutions of classical scalar field equations.

Energy gap, clustering, and the Goldstone theorem in statistical mechanics

We prove a Goldstone-type theorem for a wide class of lattice and continuum quantum systems, both for the ground state and at nonzero temperature. For the ground state (T=0) spontaneous breakdown of a continuous symmetry implies no energy gap. For nonzero temperature, spontaneous symmetry breakdown implies slow clustering (noL1 clustering). The methods apply also to nonzero-temperature classical systems.

Localization in the ground state of the Ising model with a random transverse field

AbstractWe study the zero-temperature behavior of the Ising model in the presence of a random transverse field. The Hamiltonian is given by

Fluctuations in the Curie-Weiss version of the random field Ising model

H = - J\sum\limits_{\left\langle {x,y} \right\rangle } {\sigma _3 (x)\sigma _3 (y) - \sum\limits_x {h(x)\sigma _1 (x)} }

The Mermin-Wagner Phenomenon and Cluster Properties of One- and Two-Dimensional Systems

whereJ>0,x,y∈Zd, σ1, σ3 are the usual Pauli spin 1/2 matrices, andh={h(x),x∈Zd} are independent identically distributed random variables. We consider the ground state correlation function 〈σ3(x)σ3(y)〉 and prove:1.Letd be arbitrary. For anym>0 andJ sufficiently small we have, for almost every choice of the random transverse fieldh and everyx∈Zd, that