arXiv subjects

Martin P. Gelfand

Publications and source records attributed to Martin P. Gelfand.

11 recordsLinked to original sources

arXiv2010

Simple Vortex States in Films of Type-I Ginzburg-Landau Superconductor

Sufficiently thin films of type-I superconductor in a perpendicular magnetic field exhibit a triangular vortex lattice, while thick films develop an intermediate state. To elucidate what happens between these two regimes, precise numerical calculations have been made within Ginzburg-Landau theory at $κ=0.5$ and 0.25 for a variety of vortex lattice structures with one flux quantum per unit cell. The phase diagram in the space of mean induction and film thickness includes a narrow wedge in which a square lattice is stable, surrounded by the domain of stability of the triangular lattice at thinner films/lower fields and, on the other side, rectangular lattices with continuously varying aspect ratio. The vortex lattice has an anomalously small shear modulus within and close to the square lattice phase.

cond-mat.supr-con↗

arXiv2000

Finite-size calculations of spin-lattice relaxation rates in Heisenberg spin-ladders

Calculations of nuclear spin-lattice relaxation rates are carried out by means of exact diagonalization on small (2 x 6) antiferromagnetic Heisenberg ladders, using the simplest forms permitted by symmetry for the hyperfine couplings for the three nuclear sites in Cu2O3 ladders. Several values of the rung/chain exchange ratio have been considered. Comparisons with experimental results, field theoretic calculations, and the Gaussian approximation highlight some open problems.

cond-mat.str-el↗

arXiv1998

Bond-Operator Mean Field Theory for the Bilayer Heisenberg Model

Bond-operator mean field equations for the square-lattice, S=1/2 bilayer Heisenberg model are developed and solved numerically. In the vicinity of both the zero-field critical point and the field-induced transitions, comparisons are made with T=0 and finite-temperature strong coupling expansions. The mean-field theory suggests that the quantum critical region for the field-induced transitions is restricted to significantly lower temperatures than one might have concluded based on strong-coupling expansions or other numerical studies.

cond-mat.str-el↗

arXiv1997

Phase Transitions in Bilayer Heisenberg Model with General Couplings

The ground state properties and phase diagram of the bilayer square-lattice Heisenberg model are studied in a broad parameter space of intralayer exchange couplings, assuming an antiferromagnetic coupling between constituent layers. In the classical limit, the model exhibits three phases: two of these are ordered phases specified by the ordering wave vectors (pi,pi;pi) and (0,0;pi), where the third component of each indecates the antiferromagnetic orientation between layers, while another one is a canted phase, stabilized by competing interactions. The effects of quantum fluctuations in the model with S=1/2 have been explored by means of dimer mean-field theory, small-system exact diagonalization, and high-order perturbation expansions about the interlayer dimer limit.

cond-mat.str-el↗

arXiv1997

Spin-S bilayer Heisenberg models: Mean-field arguments and numerical calculations

Spin-S bilayer Heisenberg models (nearest-neighbor square lattice antiferromagnets in each layer, with antiferromagnetic interlayer couplings) are treated using dimer mean-field theory for general S and high-order expansions about the dimer limit for S=1, 3/2,...,4. We suggest that the transition between the dimer phase at weak intraplane coupling and the Neel phase at strong intraplane coupling is continuous for all S, contrary to a recent suggestion based on Schwinger boson mean-field theory. We also present results for S=1 layers based on expansions about the Ising limit: In every respect the S=1 bilayers appear to behave like S=1/2 bilayers, further supporting our picture for the nature of the order-disorder phase transition.

cond-mat↗

arXiv1997

Tests of magnetic Hamiltonians for CaV_4O_9

We study the uniform magnetic susceptibility and spin-gap for recently proposed Heisenberg model Hamiltonians for CaV_4O_9 based on the orbital ordering scenario of Marini and Khomskii and the LDA calculations of Pickett. We argue that the experimentally observed uniform susceptibility data is inconsistent with the weakly coupled dimer picture of Marini and Khomskii. The model proposed by Pickett can, with appropriate choice of parameters, lead to an explanation for the observed gap and uniform susceptibility. The resulting agreement with experiments is of a similar quality to previously studied models. We argue that this new model is best distinguished from previous ones by neutron or Raman scattering experiments, via the location of the excitation minimum in the Brillouin zone and by the possible existence or non-existence of sharply defined singlet excitations.

cond-mat.str-el↗

arXiv1996

Local susceptibilities in semi-infinite antiferromagnet chains: elementary perspectives

Using conformal field theory methods Eggert and Affleck have shown that the semi-infinite S=1/2 Heisenberg antiferromagnetic chain exhibits a remarkable alternation in its local response to a uniform field at low temperatures. Such alternation is not an essentially quantum effect: similar, and sometimes stronger, susceptibility alternation is a feature of classical Heisenberg-Ising chains at T=0. In S=1/2 chains, susceptibility alternation is not unique to the Heisenberg model, but can be seen in expansions about the Ising model and also in the XY model.

cond-mat↗

arXiv1995

Spin-wave excitation spectra and spectral weights in square lattice antiferromagnets

Using a recently developed method for calculating series expansions of the excitation spectra of quantum lattice models, we obtain the spin-wave spectra for square lattice, $S=1/2$ Heisenberg-Ising antiferromagnets. The calculated spin-wave spectrum for the Heisenberg model is close to but noticeably different from a uniformly renormalized classical (large-$S$) spectrum with the renormalization for the spin-wave velocity of approximately $1.18$. The relative weights of the single-magnon and multi-magnon contributions to neutron scattering spectra are obtained for wavevectors throughout the Brillouin zone.

cond-mat↗

arXiv1995

Series Expansions for Excited States of Quantum Lattice Models

We show that by means of connected-graph expansions one can effectively generate exact high-order series expansions which are informative of low-lying excited states for quantum many-body systems defined on a lattice. In particular, the Fourier series coefficients of elementary excitation spectra are directly obtained. The numerical calculations involved are straightforward extensions of those which have already been used to calculate series expansions for ground-state correlations and $T=0$ susceptibilities in a wide variety of models. As a test, we have reproduced the known elementary excitation spectrum of the transverse-field Ising chain in its disordered phase.

cond-mat↗

arXiv1995

Phase Transitions in the Symmetric Kondo Lattice Model in Two and Three Dimensions

We present an application of high-order series expansion in the coupling constants for the ground state properties of correlated lattice fermion systems. Expansions have been generated up to order $(t/J)^{14}$ for $d=1$ and $(t/J)^8$ for $d=2,\ 3$ for certain properties of the symmetric Kondo lattice model. Analyzing the susceptibility series, we find evidence for a continuous phase transition from the ``spin liquid'' phase characteristic of a ``Kondo Insulator'' to an antiferromagnetically ordered phase in dimensions $d\ge2$ as the antiferromagnetic Kondo coupling is decreased. The critical point is estimated to be at $(t/J)_c\approx0.7$ for square lattice and $(t/J)_c\approx0.5$ for simple-cubic lattice.

cond-mat↗

arXiv1994

A Plane of Weakly Coupled Heisenberg Chains: Theoretical Arguments and Numerical Calculations

The $S=1/2$, nearest-neighbor, quantum Heisenberg antiferromagnet on the square lattice with spatially anisotropic couplings is reconsidered, with particular attention to the following question: at T=0, does Néel orderdevelop at infinitesimal interchain coupling, or is there a nonzero critical coupling? A heuristic renormalization group argument is presented which suggests that previous theoretical answers to that question are incorrect or at least incomplete, and that the answer is not universal but rather depends on the microscopic details of the model under consideration. Numerical investigations of the nearest-neighbor model are carried out {\it via} zero-temperature series expansions about Ising and dimer Hamiltonians. The results are entirely consistent with a vanishing critical interchain coupling ratio $R_c$; if $R_c$ is finite, it is unlikely to substantially exceed 0.02.

cond-mat↗