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Akademie Verlag eBooks

Theory of spine latticesand lattice gauge models : 165th WE-Heraeus Seminar, held at Physikzentrum Bad Honnef, Germany, October 14-16, 1996

J. W. Clark, MANFRED L. RISTIG

Published Jan 1, 1997• 0 citations
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Abstract

Ising, Heisenberg and Hubbard models in relation to insulating and metallic ferro- and antiferro-magnets studies of lattice spin systems using series expansions application of linked-cluster expansions to quantum Hamiltonian lattice systems critical properties of 1-D spin 1/2 antiferro-magnetic Heisenberg model the Z(2) lattice gauge vacuum and the transverse Ising model crystallographic point and space group symmetries in correlated many-body wave functions Hamiltonian lattice calculations on gauge and chiral meson field theories.

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Quantum inversion theory and applications : proceedings of the 109th W.E. Heraeus Seminar held at Bad Honnef, Germany, May 17-19, 1993

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Cluster expansions for the Ising and Heisenberg spin models in Hamiltonian lattice field theory

Chris J. Hamer, Anthony John Guttmann

Cluster expansion methods are applied to calculate 'high-temperature' series for the vacuum energy, the susceptibility and the mass gap for the Ising model and the O(2) and O(3) Heisenberg models in (1+1) dimensions and (2+1) dimensions. Critical points and critical indices are estimated for the line, the square and the triangular lattices. The results demonstrate universality with the normal Euclidean versions of these models, within errors.

Journal of Physics A Mathematical and General•Sep 7, 1989•9 citations

Field theory and collective phenomena : in memory of professor Hiroomi Umezawa, perugia, Italy, 28-31 May, 1992

S. De Lillo, 博臣 梅沢

Fullerene: symmetries and symmetry breaking, M. Rasetti flux dynamics in 2-dimensional arrays of Josephson junctions, A.R. Bishop the magnetic field dependence of the SDW transport in organic conductors, K. Maki Peierls substitution and Chern-Simons quantum mechanics, G. Dunne and R. Jackiw quantum solids by means of effective potentials, V. Tognetti Path integral approach to classical mechanics and Toda criterion, E. Gozzi et al integrable systems of coupled nonlinear ODEs and PDEs and solvable nonlinear integrodifferential equations of Boltzmann type, F. Calogero asymptotic formulae for cycles in the quadratic map, J. Stephenson cavity methods for mean field spin glasses, F. Guerra c-calculus and fuzzy measures, E. R. Caianiello remarks on constructing a measure for Yang-Mills fields, G.F. Dell'Antonio physical states of unbroken gauge symmetry, M.H. Friedman et al chiral symmetry breaking in lattice QED, G.W. Semenoff a united framework for quantum stochastic differential equations within nonequilibrium thermofield dynamics, T. Arimitsu gauge theory for thermal Bogolubov transformation, K. Nakamura dynamical rearrangement of symmetries in nuclei, F.C. Khanna. (Part contents)

WORLD SCIENTIFIC eBooks•Jan 1, 1995•0 citations

Linked-cluster expansions for quantum magnets on the hypercubic lattice

K. Coester, Darshan G. Joshi, Matthias Vojta C +1 more

For arbitrary space dimension $d$, we investigate the quantum phase transitions of two paradigmatic spin models defined on a hypercubic lattice, the coupled-dimer Heisenberg model and the transverse-field Ising model. To this end, high-order linked-cluster expansions for the ground-state energy and the one-particle gap are performed up to order 9 about the decoupled-dimer and high-field limits, respectively. Extrapolations of the high-order series yield the location of the quantum phase transition and the correlation-length exponent $\ensuremath{\nu}$ as a function of space dimension $d$. The results are complemented by $1/d$ expansions to next-to-leading order of observables across the phase diagrams. Remarkably, our analysis of the extrapolated linked-cluster expansion allows to extract the coefficients of the full $1/d$ expansion for the phase-boundary location in both models exactly in leading order and quantitatively for subleading corrections.

arXiv:1605.05848•Physical review. B./Physical review. B•Sep 6, 2016•17 citations

Theory of Spin Lattices and Lattice Gauge Models

J. W. Clark, MANFRED L. RISTIG

Springer eBooks•Jan 1, 1997•9 citations
Ising, Heisenberg and Hubbard models in relation to insulating and metallic ferro- and antiferro-magnets studies of lattice spin systems using series expansions application of linked-cluster expansions to quantum Hamiltonian lattice systems critical properties of 1-D spin 1/2 antiferro-magnetic Heisenberg model the Z(2) lattice gauge vacuum and the transverse Ising model crystallographic point and space group symmetries in correlated many-body wave functions Hamiltonian lattice calculations on gauge and chiral meson field theories.
Introductory many-body theory, D.J. Thouless collective description of many-body systems, R.M. Dreizler fermi liquid theory, D. Pines theory of fractional quantum hall effect, A.H. MacDonald numerical methods for problems of interacting many electron systems, D.J. Scalapino supersymmetry in nuclear and condensed matter physics, A.B. Balantekin strongly coupled plasmas, K.I. Golden fractional quantum hall effect and electron solid, R.G. Clark models to treat strong electronic correlations, M.P. Das physics of anyons, R.B. Laughlin. (Part contents).
Fullerene: symmetries and symmetry breaking, M. Rasetti flux dynamics in 2-dimensional arrays of Josephson junctions, A.R. Bishop the magnetic field dependence of the SDW transport in organic conductors, K. Maki Peierls substitution and Chern-Simons quantum mechanics, G. Dunne and R. Jackiw quantum solids by means of effective potentials, V. Tognetti Path integral approach to classical mechanics and Toda criterion, E. Gozzi et al integrable systems of coupled nonlinear ODEs and PDEs and solvable nonlinear integrodifferential equations of Boltzmann type, F. Calogero asymptotic formulae for cycles in the quadratic map, J. Stephenson cavity methods for mean field spin glasses, F. Guerra c-calculus and fuzzy measures, E. R. Caianiello remarks on constructing a measure for Yang-Mills fields, G.F. Dell'Antonio physical states of unbroken gauge symmetry, M.H. Friedman et al chiral symmetry breaking in lattice QED, G.W. Semenoff a united framework for quantum stochastic differential equations within nonequilibrium thermofield dynamics, T. Arimitsu gauge theory for thermal Bogolubov transformation, K. Nakamura dynamical rearrangement of symmetries in nuclei, F.C. Khanna. (Part contents)
For arbitrary space dimension ddd, we investigate the quantum phase transitions of two paradigmatic spin models defined on a hypercubic lattice, the coupled-dimer Heisenberg model and the transverse-field Ising model. To this end, high-order linked-cluster expansions for the ground-state energy and the one-particle gap are performed up to order 9 about the decoupled-dimer and high-field limits, respectively. Extrapolations of the high-order series yield the location of the quantum phase transition and the correlation-length exponent $\ensuremath{\nu}$ as a function of space dimension ddd. The results are complemented by 1/d1/d1/d expansions to next-to-leading order of observables across the phase diagrams. Remarkably, our analysis of the extrapolated linked-cluster expansion allows to extract the coefficients of the full 1/d1/d1/d expansion for the phase-boundary location in both models exactly in leading order and quantitatively for subleading corrections.