BRST-anti-BRST Antifield formalism : The Example of the Freedman-Townsend Model

The general BRST-anti-BRST construction in the framework of the antifield-antibracket formalism is illustrated in the case of the Freedmann-Townsend model.Comment: 16 pages, Latex file, Latex errors corrected, otherwise unchange

Algebraic Properties of BRST Coupled Doublets

We characterize the dependence on doublets of the cohomology of an arbitrary nilpotent differential s (including BRST differentials and classical linearized Slavnov-Taylor (ST) operators) in terms of the cohomology of the doublets-independent component of s. All cohomologies are computed in the space of local integrated formal power series. We drop the usual assumption that the counting operator for the doublets commutes with s (decoupled doublets) and discuss the general case where the counting operator does not commute with s (coupled doublets). The results are purely algebraic and do not rely on power-counting arguments.Comment: Some explanations enlarged, references adde

Available energy from diffusive and reversible phase space rearrangements

Rearranging the six-dimensional phase space of particles in plasma can release energy. The rearrangement may happen through the application of electric and magnetic fields, subject to various constraints. The maximum energy that can be released through a rearrangement of a distribution of particles can be called its available or free energy. Rearrangement subject to phase space volume conservation leads to the classic Gardner free energy. Less free energy is available when constraints are applied, such as respecting conserved quantities. Also, less energy is available if particles can only be diffused in phase-space from regions of high phase-space density to regions of lower phase-space density. The least amount of free energy is available if particles can only be diffused in phase space, while conserved quantities still need to be respected.Comment: 7 pages, 3 figure

Power-law correlations and orientational glass in random-field Heisenberg models

Monte Carlo simulations have been used to study a discretized Heisenberg ferromagnet (FM) in a random field on simple cubic lattices. The spin variable on each site is chosen from the twelve [110] directions. The random field has infinite strength and a random direction on a fraction x of the sites of the lattice, and is zero on the remaining sites. For x = 0 there are two phase transitions. At low temperatures there is a [110] FM phase, and at intermediate temperature there is a [111] FM phase. For x > 0 there is an intermediate phase between the paramagnet and the ferromagnet, which is characterized by a |k|^(-3) decay of two-spin correlations, but no true FM order. The [111] FM phase becomes unstable at a small value of x. At x = 1/8 the [110] FM phase has disappeared, but the power-law correlated phase survives.Comment: 8 pages, 12 Postscript figure

Subextensive singularity in the 2D ±J\pm J Ising spin glass

The statistics of low energy states of the 2D Ising spin glass with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le 48$, and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. The behavior of the density of states near the ground state energy is analyzed as a function of $L$, in order to obtain the low temperature behavior of the model. For large finite $L$ there is a range of $T$ in which the heat capacity is proportional to $T^{5.33 \pm 0.12}$. The range of $T$ in which this behavior occurs scales slowly to $T = 0$ as $L$ increases. Similar results are found for $p$ = 0.25. Our results indicate that this model probably obeys the ordinary hyperscaling relation $d \nu = 2 - \alpha$, even though $T_c = 0$. The existence of the subextensive behavior is attributed to long-range correlations between zero-energy domain walls, and evidence of such correlations is presented.Comment: 13 pages, 7 figures; final version, to appear in J. Stat. Phy

Power-law correlated phase in random-field XY models and randomly pinned charge-density waves

Monte Carlo simulations have been used to study the Z6 ferromagnet in a random field on simple cubic lattices, which is a simple model for randomly pinned charge-density waves. The random field is chosen to have infinite strength on a fraction x of the sites of the lattice, and to be zero on the remaining sites. For x= 1/16 there are two phase transitions. At low temperature there is a ferromagnetic phase, which is stabilized by the six-fold nonrandom anisotropy. The intermediate temperature phase is characterized by a |k|^(-3) decay of two-spin correlations, but no true ferromagnetic order. At the transition between the power-law correlated phase and the paramagnetic phase the magnetic susceptibility diverges, and the two-spin correlations decay approximately as |k|^(-2.87).Comment: 16 pages, 8 figures, Postscrip

Topological Defects in the Random-Field XY Model and the Pinned Vortex Lattice to Vortex Glass Transition in Type-II Superconductors

As a simplified model of randomly pinned vortex lattices or charge-density waves, we study the random-field XY model on square ($d=2$) and simple cubic ($d=3$) lattices. We verify in Monte Carlo simulations, that the average spacing between topological defects (vortices) diverges more strongly than the Imry-Ma pinning length as the random field strength, $H$, is reduced. We suggest that for $d=3$ the simulation data are consistent with a topological phase transition at a nonzero critical field, $H_c$, to a pinned phase that is defect-free at large length-scales. We also discuss the connection between the possible existence of this phase transition in the random-field XY model and the magnetic field driven transition from pinned vortex lattice to vortex glass in weakly disordered type-II superconductors.Comment: LATEX file; 5 Postscript figures are available from [email protected]