Dr. Miron Kaufman
Cleveland State University, Cleveland, OH., USA
Professor Emeritus
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Academic Career Length
51Years (1976-Present)
(Calculated once Scilit publication data is synced: current year − year of first publication + 1)
Representative Publications
View All Publications1 November 1982 in Physical Review B
Journal Article
RGRobert B. Griffiths
Robert B. Griffiths
Miron KaufmanA number of exactly soluble models in statistical mechanics can be produced with the use of spins interacting with nearest neighbors on a hierarchical lattice. A general definition and several examples of such lattices are given, and the topological properties of one of these, the "diamond" lattice, are discussed in detail. It is shown that the free energy has a well-defined thermodynamic limit for a large class of discrete spin models on hierarchical lattices.
1 July 1981 in Physical Review B
Journal Article
Miron KaufmanRGRobert B. Griffiths
Robert B. Griffiths
Certain approximate renormalization-group recursion relations are exact for Ising models on special hierarchical lattices, as noted by Berker and Ostlund. These lattice models provide numerous examples of phase coexistence and critical points at finite temperatures, including cases of continuously varying critical exponents and phase transitions without phase coexistence. The lattices are, typically, quite inhomogeneous and may possess several inequivalent limits as infinite lattices.
1 July 1984 in Physical Review B
Journal Article
Miron KaufmanRGRobert B. Griffiths
Robert B. Griffiths
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.
11 October 2006 in Macromolecular Theory and Simulations
Journal Article
1 April 1981 in Physical Review B
Journal Article
Miron KaufmanRGRobert B. Griffiths
Robert B. Griffiths
JYJulia M. Yeomans
Julia M. Yeomans
MFMichael E. Fisher
Michael E. Fisher
The global phase diagram for a three-component lattice gas or spin-one Ising model with general single-site and nearest-neighbor "ferromagnetic" interactions is worked out for two-dimensional lattices using a Migdal-Kadanoff recursion relation. It differs in important qualitative respects from the corresponding mean-field phase diagram. The set of fixed points and flows provides the characteristic phase diagrams of the three-state Potts multicritical point and the ordinary () tricritical point in a complete set of symmetry-breaking fields. The latter is associated, in this renormalization-group scheme, with seven distinct critical fixed points, a number which is surprisingly large.
1 October 1986 in Physical Review B
Journal Article
The phase diagram of the mean-field Ising model in a random field obeying a symmetric three-peak distribution is determined. This distribution is relevant to diluted antiferromagnets in a uniform magnetic field. The phase diagram includes a fourth-order point, tricritical points, ordered critical points, critical end points, and a double critical end point. An ordered phase persists for arbitrarily large random fields at low temperatures.
About Me
Dr. Kaufman joined Cleveland State University in 1985 and has been a full professor since 1995. From 2000 to 2012, he chaired the Physics Department. He retired in 2021 to become professor emeritus.
Dr. Kaufman's research in statistical physics covers topics in superconductivity, magnetism, multicritical points, liquids, polymers, hierarchical and fractal lattices, and sociophysics.
He has also collaborated on several National Science Foundation and National Institute of Health-funded research projects at the interface of statistical physics with cognitive science, health science, urban studies, and engineering. His publications have been referenced 3000 times and his Hirsch index is 27.