March 31, 2010 Wednesday 15:30
A. Nihat Berker, Sabanci University
Inverted Tricriticality and Apollonian Tulips in A Plenitude of Exactly Soluble Statistical Mechanics with Quenched Randomness

Abstract: The distinctive phase transition phenomena of magnetic systems with frozen disorder are studied with renormalization-group theories that are numerically exact for d=3 hierarchical lattices and that have proven to be quite indicative for the physical lattices. A pedagogical introduction will be followed by recent results, including inverted tricritical points [1], finite-temperature spin-glass order induced by quenched dilution, asymmetric quantum spin-glass phase diagrams. On scale-free small-world spin-glass networks, the calculated local magnetizations and local spin-glass order parameters exhibit, as function of temperature, complex tulip patterns.[2] The conversion of first-order phase transitions to second order and the strong violation of critical phenomena universality, predicted by this approach, has recently been confirmed by numerical simulation.[3]
[1] V.O. Özçelik and A.N. Berker, Phys. Rev. E 78, 031104 (2008).
[2] C.N. Kaplan, M. Hinczewski, and A.N. Berker, Phys. Rev. E 79, 061120 (2009).
[3] A. Malakis, A.N. Berker, I.A. Hadjiagapiou, and N.G. Fytas, Phys. Rev. E 79, 011125 (2009).