Properties of phase transitions of higher order

There is only limited experimental evidence for the existence in nature of phase transitions of Ehrenfest order greater than two. However, there is no physical reason for their non-existence, and such transitions certainly exist in a number of theoretical models in statistical physics and lattice field theory. Here, higher-order transitions are analysed through the medium of partition function zeros. Results concerning the distributions of zeros are derived as are scaling relations between some of the critical exponents.Comment: 6 pages, poster presented at Lattice 2005 (Spin and Higgs), Trinity College Dubli

Decorating Random Quadrangulations

On various regular lattices (simple cubic, body centred cubic..) decorating an edge with an Ising spin coupled by bonds of strength L to the original vertex spins and competing with a direct anti-ferromagnetic bond of strength alpha L can give rise to three transition temperatures for suitable alpha. The system passes through ferromagnetic, paramagnetic, anti-ferromagnetic and paramagnetic phases respectively as the temperature is increased. For the square lattice on the other hand multiple decoration is required to see this effect. We note here that a single decoration suffices for the Ising model on planar random quadrangulations (coupled to 2D quantum gravity). Other random bipartite lattices such as the Penrose tiling are more akin to the regular square lattice and require multiple decoration to have any affect.Comment: 6 pages + 5 figure

Study, definition and analysis of pilot/system performance measurements for planetary entry experiments

Definition analysis for experimental prediction of pilot performance during planetary entr

Potts Models with (17) Invisible States on Thin Graphs

The order of a phase transition is usually determined by the nature of the symmetry breaking at the phase transition point and the dimension of the model under consideration. For instance, q-state Potts models in two dimensions display a second order, continuous transition for q = 2,3,4 and first order for higher q. Tamura et al recently introduced Potts models with "invisible" states which contribute to the entropy but not the internal energy and noted that adding such invisible states could transmute continuous transitions into first order transitions. This was observed both in a Bragg-Williams type mean-field calculation and 2D Monte-Carlo simulations. It was suggested that the invisible state mechanism for transmuting the order of a transition might play a role where transition orders inconsistent with the usual scheme had been observed. In this paper we note that an alternative mean-field approach employing 3-regular random ("thin") graphs also displays this change in the order of the transition as the number of invisible states is varied, although the number of states required to effect the transmutation, 17 invisible states when there are 2 visible states, is much higher than in the Bragg-Williams case. The calculation proceeds by using the equivalence of the Potts model with 2 visible and r invisible states to the Blume-Emery-Griffiths (BEG) model, so a by-product is the solution of the BEG model on thin random graphs.Comment: (2) Minor typos corrected, references update

Oscillating magnetoresistance due to fragile spin structure in metallic GdPd3_3

Studies on the phenomenon of magnetoresistance (MR) have produced intriguing and application-oriented outcomes for decades--colossal MR, giant MR and recently discovered extremely large MR of millions of percents in semimetals can be taken as examples. We report here the investigation of oscillating MR in a cubic intermetallic compound GdPd$_3$, which is the only compound that exhibits MR oscillations between positive and negative values. Our study shows that a very strong correlation between magnetic, electrical and magnetotransport properties is present in this compound. The magnetic structure in GdPd$_3$ is highly fragile since applied magnetic fields of moderate strength significantly alter the spin arrangement within the system--a behavior that manifests itself in the oscillating MR. Intriguing magnetotransport characteristics of GdPd$_3$ are appealing for field-sensitive device applications, especially if the MR oscillation could materialize at higher temperature by manipulating the magnetic interaction through perturbations caused by chemical substitutions.Comment: 10 pages, 7 figures. A slightly modified version is published in Scientific Report