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Upper Bound on the Truncated Connectivity in One-Dimenional β/|x-y|² Percolation Models at β > 1
- 1. Rev. Math. Phys
, 1995
"... We consider one-dimensional Fortuin-Kasteleyn percolation models generated by the bond occupation probabilities p (xy) = ae p if jx \Gamma yj = 1 1 \Gamma e \Gammafi=jx\Gammayj 2 otherwise and a real parameter . We prove that for any fi ? 1 and 1 the percolation density M is strictly positive ..."
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Cited by 5 (1 self)
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We consider one-dimensional Fortuin-Kasteleyn percolation models generated by the bond occupation probabilities p (xy) = ae p if jx \Gamma yj = 1 1 \Gamma e \Gammafi=jx\Gammayj 2 otherwise and a real parameter . We prove that for any fi ? 1 and 1 the percolation density M is strictly
Improved Lower Bound On The Thermodynamic Pressure Of The Spin 1/2 Heisenberg Ferromagnet
"... . We introduce a new stochastic representation of the partition function of the spin 1/2 Heisenberg ferromagnet. We express some of the relevant thermodynamic quantities in terms of expectations of functionals of so called random stirrings on Z d . By use of this representation we improve the lowe ..."
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Cited by 28 (0 self)
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jx\Gammayj=1 h (S(x) \Gamma S(y)) 2 \Gamma 1 i (1.1) where S(x) = (S X (x); S Y (x); S Z (x)) ; x 2 , are the local spin operators and the summation runs over nearest neighbour pairs of lattice sites in the rectangular box , with periodic boundary conditions. The canonical commutation relations
A Continuum Approximation for the Excitations of the (1, 1, ..., 1) Interface in the Quantum Heisenberg model
, 1999
"... : It is shown that, with an appropriate scaling, the energy of lowlying excitations of the (1; 1; : : : ; 1) interface in the d-dimensional quantum Heisenberg model are given by the spectrum of the d \Gamma 1-dimensional Laplacian on an suitable domain. Keywords: Anisotropic Heisenberg ferromagnet, ..."
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Cited by 2 (1 self)
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the spin 1/2 XXZ Heisenberg model on the d-dimensional lattice Z d . For any finite volume ae Z d , the Hamiltonian is given by H = \Gamma X x;y2 jx\Gammayj=1 \Delta \Gamma1 (S (1) x S (1) y + S (2) x S (2) y ) + S (3) x S (3) y ; (1.1) where \Delta ? 1 is the anisotropy. We refer
The Low-Temperature Limit Of Transfer Operators In Fixed Dimension
"... . We construct the 0'th order low-temperature WKB-phase for the first eigenfunction of a transfer operator in a large domain around a non-degenerate critical point for the potential. The 0'th order low-temperature phase is shown to solve the eikonal equation in the strong-coupling limit an ..."
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Cited by 1 (0 self)
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J 2 jx\Gammayj 2 e \Gamma fi 2 V (y) ; where fi is the inverse temperature, J is a coupling constant...
Absence of Phase Transitions in Two-Dimensional O(N) Spin Models with Large N
"... so that Z = exp[\GammaW 0 (OE; /)] dOE(x)d/(x); (3) W 0 = 1 ! OE; (\Gamma\Delta +m )OE ? \Gammai ! J 0 ; / ?; (4) J 0 (x) = \Gamma : OE (x) : G0 = N fi \Gamma OE (x); (5) where \Delta xy = \Gamma4ffi xy + ffi jx\Gammayj;1 is the lattice laplacian on Z , G 0 (x; y) = (\Gamma\ ..."
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so that Z = exp[\GammaW 0 (OE; /)] dOE(x)d/(x); (3) W 0 = 1 ! OE; (\Gamma\Delta +m )OE ? \Gammai ! J 0 ; / ?; (4) J 0 (x) = \Gamma : OE (x) : G0 = N fi \Gamma OE (x); (5) where \Delta xy = \Gamma4ffi xy + ffi jx\Gammayj;1 is the lattice laplacian on Z , G 0 (x; y) = (\Gamma
