Induced Saturation Number

In this paper, we discuss a generalization of the notion of saturation in graphs in order to deal with induced structures. In particular, we define ${\rm indsat}(n,H)$, which is the fewest number of gray edges in a trigraph so that no realization of that trigraph has an induced copy of $H$, but changing any white or black edge to gray results in some realization that does have an induced copy of $H$. We give some general and basic results and then prove that ${\rm indsat}(n,P_4)=\lceil (n+1)/3\rceil$ for $n\geq 4$ where $P_4$ is the path on 4 vertices. We also show how induced saturation in this setting extends to a natural notion of saturation in the context of general Boolean formulas.Comment: 14 pages, 7 figure

Brownian-Vacancy Mediated Disordering Dynamics

The disordering of an initially phase segregated system of finite size, induced by the presence of highly mobile vacancies, is shown to exhibit dynamic scaling in its late stages. A set of characteristic exponents is introduced and computed analytically, in excellent agreement with Monte Carlo data. In particular, the characteristic time scale, controlling the crossover between increasing disorder and saturation, is found to depend on the exponent scaling the number of vacancies in the sample.Comment: 6 pages, typeset using Euro-LaTex, 6 figures, compresse

Enhanced magnetocaloric effect in frustrated magnets

The magnetothermodynamics of strongly frustrated classical Heisenberg antiferromagnets on kagome, garnet, and pyrochlore lattices is examined. The field induced adiabatic temperature change (dT/dH)_S is significantly larger for such systems compared to ordinary non-frustrated magnets and also exceeds the cooling rate of an ideal paramagnet in a wide range of fields. An enhancement of the magnetocaloric effect is related to presence of a macroscopic number of soft modes in frustrated magnets below the saturation field. Theoretical predictions are confirmed with extensive Monte Carlo simulations.Comment: 7 page