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PRESENTED AT THE 2009 IEEE WORKSHOP ON STATISTICAL SIGNAL PROCESSING, CARDIFF, WALES LOOKING THROUGH WAVELETS TO VIEW THE ISING PROBLEM
"... While there exist many coarsegraining techniques for accelerating Molecular Dynamic and Monte Carlo simulations, the rich structure and scaling properties of wavelets have found limited use in these techniques, especially in their investigating of thermodynamic properties of materials. To promote e ..."
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wavelets, as also wavelet packets to coarsely grain the 2D finite size Ising model. Thermodynamic properties are then calculated to predict, in some sense, potential for phase transition. Exact calculations are confirmed using Monte Carlo simulations. Based on these results we propose a number of wavelet
Thermodynamics of spin chains of Haldane–Shastry type and onedimensional vertex models
"... We study the thermodynamic properties of spin chains of Haldane–Shastry type associated with the AN−1 root system in the presence of a uniform external magnetic field. To this end, we exactly compute the partition function of these models for an arbitrary finite number of spins. We then show that th ..."
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We study the thermodynamic properties of spin chains of Haldane–Shastry type associated with the AN−1 root system in the presence of a uniform external magnetic field. To this end, we exactly compute the partition function of these models for an arbitrary finite number of spins. We then show
ENTROPY OF COLORED QUARKS STATES AT FINITE TEMPERATURE
, 2007
"... The quantum entropy at finite temperatures is analyzed by using models for colored quarks making up the physical states of the hadrons. We explicitly work out some special models for the structure of the states of SU(2)c and SU(3)c related to the effects of temperature on the quantum entropy. We sho ..."
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of strong correlations between only two of the color states. For the sake of comparison, we work out the entropy for the classical Ising and the quantum XY spin chains. In the Ising model, the quantum entropy in the ground state does not directly enter into the partition function. It also does not depend
Spin Foam Perturbation Theory for ThreeDimensional Quantum Gravity
, 2008
"... We formulate the spin foam perturbation theory for threedimensional Euclidean Quantum Gravity with a cosmological constant. We analyse the perturbative expansion of the partition function in the dilutegas limit and we argue that the Baez conjecture stating that the number of possible distinct topo ..."
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We formulate the spin foam perturbation theory for threedimensional Euclidean Quantum Gravity with a cosmological constant. We analyse the perturbative expansion of the partition function in the dilutegas limit and we argue that the Baez conjecture stating that the number of possible distinct
A SIMPLE WAY TO OBTAIN EXACT PROPERTIES ON THE CRITICAL FRONTIER FOR AN ANTIFERROMAGNETIC ISING MODEL ON A qCOORDINATE BETHE LATTICE
, 2005
"... An antiferromagnetic Ising model is studied on a qcoordinate Bethe lattice at the “critical frontier ” separating the ordered antiferromagnetic phase from the disordered paramagnetic phase. A simple method is used to obtain exact, closedform expressions in terms of z = exp(–2K) for the magnetizati ..."
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be calculated as being those at a site deep within a qcoordinate Cayley tree. The partition function for an Ising model on a Cayley tree with first neighbor interaction K and field H is given as [1] ( ) exp i i j i S i j i Z K H K S S H S ⎛ ⎞ ⎜ ⎟ ⎜ ⎟, ⎝ ⎠, = +, ∑ ∑ ∑ (1) where 1.iS = ± Here we consider
BITP 2003/18 ENTROPY FOR COLORED QUARK STATES AT FINITE TEMPERATURE
, 2004
"... The quantum entropy at finite temperatures is analyzed by using models for colored quarks making up the physical states of the hadrons. We explicitly work out some special models for the structure of the states of SU(2) and SU(3) relating to the effects of the temperature on the quantum entropy. We ..."
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partition function. It also does not depend on the number of spatial dimensions, but only on the number of quantum states making up the ground state. Whereas, the XY spin chain has a finite entropy at vanishing temperature. The results from the spin models qualitatively analogous to our models
On the Theory of Cooperative Phenomena
, 1953
"... The partition function of the Ising lattice which has a small number of lattice points on each side (edge) has been obtained. Such a pattition function tS convenient to consider severd general propelties of the lattice because of Its closed form. The effect of the external magnetic field, Cune point ..."
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The partition function of the Ising lattice which has a small number of lattice points on each side (edge) has been obtained. Such a pattition function tS convenient to consider severd general propelties of the lattice because of Its closed form. The effect of the external magnetic field, Cune
The interpolation method for random graphs with prescribed degrees
, 2014
"... We consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit µ with finite mean, we establish the systematic convergence of a broad class of graph parameters that includes in part ..."
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in particular the independence number, the maximum cut size and the logpartition function of the antiferromagnetic Ising and Potts models. The corresponding limits are shown to be Lipschitz and concave functions of µ. Our work extends the applicability of the celebrated interpolation method, introduced
Heisenberg models and a particular isotropic model
, 1993
"... The Heisenberg model, a quantum mechanical analogue of the Ising model, has a large ground state degeneracy, due to the symmetry generated by the total spin. This symmetry is also responsible for degeneracies in the rest of the spectrum. We discuss the global structure of the spectrum of Heisenberg ..."
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SN, consisting of permutations of the N spins in the system. In the second part of the paper we consider, as a concrete application, the model where each spin is coupled to all the other spins with equal strength. Its partition function is written as a single integral, elucidating its N
Results 11  20
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80