# WILBERT

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• 1
Electronic Resource
Amsterdam : Elsevier
Physics Letters A 94 (1983), S. 309-311
ISSN: 0375-9601
Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
Topics: Physics
Type of Medium: Electronic Resource
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• 2
Electronic Resource
Springer
Communications in mathematical physics 39 (1974), S. 185-205
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract We consider a two-dimensional Ising ferromagnet with (+) boundary conditions and negative external field, where a Markovian time evolution is assumed. We construct, suitably restricting the allowed configurations att=0, a non equilibrium state with positive magnetization such that: 1) only one phase is present, 2) the relaxation time for unit volume is finite and can be made very large. These results are obtained following a general method for describing metastable states proposed by Lebowitz and Penrose and exploiting the analysis of the Ising-spin-configurations in terms of contours given by Minlos and Sinai.
Type of Medium: Electronic Resource
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• 3
Electronic Resource
Springer
Communications in mathematical physics 111 (1987), S. 555-577
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract WE consider a one-dimensional random Ising model with Hamiltonian $$H = \sum\limits_{i\ddag j} {\frac{{J_{ij} }}{{\left| {i - j} \right|^{1 + \varepsilon } }}S_i S_j } + h\sum\limits_i {S_i }$$ , where ε〉0 andJ ij are independent, identically distributed random variables with distributiondF(x) such that i) $$\int {xdF\left( x \right) = 0}$$ , ii) $$\int {e^{tx} dF\left( x \right)〈 \infty \forall t \in \mathbb{R}}$$ . We construct a cluster expansion for the free energy and the Gibbs expectations of local observables. This expansion is convergent almost surely at every temperature. In this way we obtain that the free energy and the Gibbs expectations of local observables areC ∞ functions of the temperature and of the magnetic fieldh. Moreover we can estimate the decay of truncated correlation functions. In particular for every ε′〉0 there exists a random variablec(ω)m, finite almost everywhere, such that $$\left| {\left\langle {s_0 s_j } \right\rangle _H - \left\langle {s_0 } \right\rangle _H \left\langle {s_j } \right\rangle _H } \right| \leqq \frac{{c\left( \omega \right)}}{{\left| j \right|^{1 + \varepsilon - \varepsilon '} }}$$ , where 〈 〉 H denotes the Gibbs average with respect to the HamiltonianH.
Type of Medium: Electronic Resource
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• 4
Electronic Resource
Springer
Communications in mathematical physics 108 (1987), S. 241-255
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract One-dimensional Ising spin systems interacting via a two-body random potential are considered; a decay with the distance like 1/r 1+ε is assumed. We consider only boundary conditions independent of the random realization of the interactions and prove uniqueness and cluster properties of Gibbs states with probability one.
Type of Medium: Electronic Resource
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• 5
Electronic Resource
Springer
Communications in mathematical physics 29 (1973), S. 219-231
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract We obtain rigorous results about the liquid-vapour phase transition. We prove that in the Lebowitz-Penrose limit the hypothesis of hard core for the interaction is not essential to reproduce the Van der Waals-Maxwell theory. It can be replaced by the superstability.
Type of Medium: Electronic Resource
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• 6
Electronic Resource
Springer
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract We consider a lattice model with a repulsive hard core and an attractive short range interaction. We show that this model has at least three independent equilibrium states, when the temperature is sufficiently low and the chemical potential is suitably chosen.
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• 7
Electronic Resource
Springer
Communications in mathematical physics 59 (1978), S. 143-166
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract We study, in the context of the Markov hyerarchical fields (d=2, 3) the role of the Markov property, of formal renormalization and of formal positivity. We determine upper and lower bounds for the ground state energy and discuss their relation with the perturbation theory series.
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• 8
Electronic Resource
Springer
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract We develop a technique for reducing the problem of the ultraviolet divergences and their removal to a free field problem. This work is an example of a problem to which a rather general method can be applied. It can be thought as an attempt towards a rigorous version (in 2 or 3 space-time dimensions) of the analysis of the structure of the functional integrals developed in [9], the underlying mechanism being essentially the same as in [11,3].
Type of Medium: Electronic Resource
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• 9
Electronic Resource
Springer
Communications in mathematical physics 80 (1981), S. 255-269
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract We consider one dimensional systems described by many body potentials with finite first moment and prove that the correlation functions are analytic in the interaction parameters. This result is not new (Dobrushin, 1973) but our proof is simpler and physically more transparent. We show that by introducing suitable blocks and averaging over the variables associated to a subset of the blocks (decimation procedure), the resulting effective interaction is such that the system can always be dealt with as a high temperature system.
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• 10
Electronic Resource
Springer
Communications in mathematical physics 87 (1982), S. 229-252
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract We consider one-dimensional spin systems with Hamiltonian: $$H\left( {\sigma _\Lambda } \right) = - \sum\limits_{t,t' \in \Lambda } {\frac{{\varepsilon _{tt'} }}{{\left| {t - t'} \right|^\alpha }}\sigma _t \sigma _{t'} - h\sum\limits_{t \in \Lambda } {\sigma _t } }$$ , where ɛ tt′ are independent random variables and, using decimation and the cluster expansion, we show that, when α〉3/2 andE(ɛ tt′ )=0, for any magnetic fieldh and inverse temperature β, the correlation functions and the free energy areC ∞ both inh and β. Moreover we discuss an example, obtained by a particular choice of the probability distribution of the ɛ tt′ 's, where the quenched magnetization isC ∞ but fails to be analytic inh for suitableh and β.
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