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Monte Carlo tests of renormalizationgroup predictions for critical phenomena in Ising models
 PHYS. REP
, 2001
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Low temperature expansion of the gonihedric Ising model” heplat/9712002. 5
, 1996
"... We investigate a model of closed (d − 1)dimensional softselfavoiding random surfaces on a ddimensional cubic lattice. The energy of a surface configuration is given by E = J(n2 + 4k n4), where n2 is the number of edges, where two plaquettes meet at a right angle and n4 is the number of edges, wh ..."
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We investigate a model of closed (d − 1)dimensional softselfavoiding random surfaces on a ddimensional cubic lattice. The energy of a surface configuration is given by E = J(n2 + 4k n4), where n2 is the number of edges, where two plaquettes meet at a right angle and n4 is the number of edges, where 4 plaquettes meet. This model can be represented as a Z2spin system with ferromagnetic nearestneighbour, antiferromagnetic nextnearestneighbour and plaquetteinteraction. It corresponds to a special case of a general class of spin systems introduced by Wegner and Savvidy. Since there is no term proportional to the surface area, the bare surface tension of the model vanishes, in contrast to the ordinary Ising model. By a suitable adaption of Peierls argument, we prove the existence of infinitely many ordered low temperature phases for the case k = 0. A low temperature expansion of the free energy in 3 dimensions up to order x 38 (x = e −βJ) shows, that for k> 0 only the ferromagnetic low temperature phases remain stable. An analysis of low temperature expansions up to order x 44 for the magnetization, susceptibility and specific heat in 3 dimensions yields critical exponents, which are in agreement with previous results. 1
0 Evaluating Grassmann Integrals
, 1998
"... I discuss a simple numerical algorithm for the direct evaluation of multiple Grassmann integrals. The approach is exact, suffers no Fermion sign problems, and allows arbitrarily complicated interactions. Memory requirements grow exponentially with the interaction range and the transverse size of the ..."
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I discuss a simple numerical algorithm for the direct evaluation of multiple Grassmann integrals. The approach is exact, suffers no Fermion sign problems, and allows arbitrarily complicated interactions. Memory requirements grow exponentially with the interaction range and the transverse size of the system. Low dimensional systems of order a thousand Grassmann variables can be evaluated on a workstation. The technique is illustrated with a spinless fermion hopping along a one dimensional chain.
PHYSICA Geometric criteria for phase transitions: The Ising
, 1996
"... model with nearest and nextnearest neighbor interactions ..."
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unknown title
, 1993
"... The crossover from first to secondorder finitesize scaling: a numerical study ..."
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The crossover from first to secondorder finitesize scaling: a numerical study
Thinking Machines Corporation
"... We compute the weak coupling expansion for the energy of the three dimensional Ising model through 48 excited bonds. We also compute the magnetization through 40 excited bonds. This was achieved via a recursive enumeration of states of fixed energy on a set of finite lattices. We use a linear combin ..."
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We compute the weak coupling expansion for the energy of the three dimensional Ising model through 48 excited bonds. We also compute the magnetization through 40 excited bonds. This was achieved via a recursive enumeration of states of fixed energy on a set of finite lattices. We use a linear combination of lattices with a generalization of helical boundary conditions to eliminate finite volume effects. Expansions about either infinite or vanishing coupling are a major technique for the study of critical properties of statistical systems and field theories. These series usually involve a diagrammatic analysis which becomes rapidly more complex as the order increases. Thus it would be interesting to have an automated technique for the generation of the relevant terms. Here we consider generating the low temperature or weak coupling expansion for discrete systems. Our approach does not involve explicit graphs, but relies on a recursive computer enumeration of configurations. We illustrate the approach on the three dimensional Ising model.
Specific Heat Exponent for the 3d Ising Model from a 24th Order High Temperature Series. by
, 1993
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SMALL PARTICLESDYNAMIC PROPERTIES OF LATTICE. PHONONS IN SMALL PARTICLES (*)
"... Rburn6. Nous pr6sentons une revue des theories et experiences des phonons dans les petits cristaux. En premier lieu, nous consid6rons les modes acoustiques et la capacite calorifique correspondante. Nous discutons aussi brikvement les vibrations optiques ainsi que l'absorption et 1'6missi ..."
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Rburn6. Nous pr6sentons une revue des theories et experiences des phonons dans les petits cristaux. En premier lieu, nous consid6rons les modes acoustiques et la capacite calorifique correspondante. Nous discutons aussi brikvement les vibrations optiques ainsi que l'absorption et 1'6mission dans l'infrarouge lointain. Abstract. Theories and experiments on phonons in small solid particles are reviewed. Acoustical modes and the corresponding vibrational specific heat are emphasized. Optical modes and the pertinent farinfrared properties are presented as well. 1. Introduction. Apart