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Comment On Aproaches To The Tricritical Point In Quasibinary Liquid Mixtures, Miron Kaufman, Robert B. Griffiths
Comment On Aproaches To The Tricritical Point In Quasibinary Liquid Mixtures, Miron Kaufman, Robert B. Griffiths
Miron Kaufman
No abstract provided.
Pseudodimensional Variation And Tricriticality Of Potts Models By Hierarchical Breaking Of Translational Invariance, Miron Kaufman, Mehran Kardar
Pseudodimensional Variation And Tricriticality Of Potts Models By Hierarchical Breaking Of Translational Invariance, Miron Kaufman, Mehran Kardar
Miron Kaufman
Potts models with equivalent- and nearest-neighbor interactions are solved exactly on Cayley trees. A parameter D is identified that plays a role similar to the spatial dimension on Bravais lattices. Breaking translational symmetry by the Cayley-tree hierarchy reduces D, leading to a changeover in the order of the phase transition via a novel tricritical point.
Spin Systems On Hierarchical Lattices. Ii. Some Examples Of Soluble Models, Miron Kaufman, Robert B. Griffiths
Spin Systems On Hierarchical Lattices. Ii. Some Examples Of Soluble Models, Miron Kaufman, Robert B. Griffiths
Miron Kaufman
Several examples are given of soluble models of phase-transition phenomena utilizing classical discrete spin systems with nearest-neighbor interaction on hierarchical lattices. These include critical exponents which depend continuously on a parameter, the Potts model on a lattice with two different coupling constants, surface tension, and excess free energy of a line of defects. In each case we point out similarities and differences with a corresponding Bravais-lattice model.
Duality And Potts Critical Amplitudes On A Class Of Hierarchical Lattices, Miron Kaufman
Duality And Potts Critical Amplitudes On A Class Of Hierarchical Lattices, Miron Kaufman
Miron Kaufman
By using the duality transformation on a class of hierarchical lattices, I show that the Potts critical amplitudes above and below the critical temperature are equal. Logarithmic modifications of the power-law singularity occur when the exponent 2—alpha is an even integer, but do not occur when 2—alpha equals an odd integer.
Short-Range And Infinite-Range Bond Percolation, Miron Kaufman, Mehran Kardar
Short-Range And Infinite-Range Bond Percolation, Miron Kaufman, Mehran Kardar
Miron Kaufman
A method for generalizing bond-percolation problems to include the possibility of infinite-range (equivalent-neighbor) bonds is presented. On Bravais lattices the crossover from nonclassical to classical (mean-field) percolation criticality in the presence of such bonds is described. The Cayley tree with nearest-neighbor and equivalent-neighbor bonds is solved exactly, and a nonuniversal line of percolation transitions with exponents dependent on nearest-neighbor bond occupation probability is observed. Points of logarithmic and exponential singularity are also encountered, and the behavior is interpreted as dimensional reduction due to the breaking of translational invariance by bonds of Cayley-tree connectivity.
Critical Amplitude Of The Potts Model: Zeroes And Divergences, Miron Kaufman, David Andelman
Critical Amplitude Of The Potts Model: Zeroes And Divergences, Miron Kaufman, David Andelman
Miron Kaufman
The critical amplitude of the q-state Potts-model free energy is studied as a function of q in two dimensions and on the diamond hierarchical lattice. The amplitude diverges at an infinite number of q values, qn,introducing logarithmic terms in the free energy. We expect that in each interval (qn,qn+1) there is a q value where the amplitude vanishes, affecting the singularity of the free energy as a function of temperature. Possible consequences for gelation and vulcanization of polymers are discussed.
Comment On Criticality Of The Anisotropic Quantum Heisenberg Model On A Self-Dual Hierarchical Lattice, Miron Kaufman, Mehran Kardar
Comment On Criticality Of The Anisotropic Quantum Heisenberg Model On A Self-Dual Hierarchical Lattice, Miron Kaufman, Mehran Kardar
Miron Kaufman
No abstract provided.
Realizable Renormalization Group And Finite-Size Scaling, Miron Kaufman, K. K. Mon
Realizable Renormalization Group And Finite-Size Scaling, Miron Kaufman, K. K. Mon
Miron Kaufman
We propose a sequence of renormalization-group transformations which are exact on hierarchical lattices and we argue, by employing finite-size scaling, that the corresponding sequence of critical exponents converges towards the exact values associated with a Bravais lattice. A test of this method is also presented.