2,795 research outputs found
The Wrong Kind of Gravity
The KPZ formula shows that coupling central charge less than one spin models
to 2D quantum gravity dresses the conformal weights to get new critical
exponents, where the relation between the original and dressed weights depends
only on the central charge. At the discrete level the coupling to 2D gravity is
effected by putting the spin models on annealed ensembles of planar random
graphs or their dual triangulations, where the connectivity fluctuates on the
same time-scale as the spins.
Since the sole determining factor in the dressing is the central charge, one
could contemplate putting a spin model on a quenched ensemble of 2D gravity
graphs with the ``wrong'' central charge. We might then expect to see the
critical exponents appropriate to the central charge used in generating the
graphs. In such cases the KPZ formula could be interpreted as giving a
continuous line of critical exponents which depend on this central charge. We
note that rational exponents other than the KPZ values can be generated using
this procedure for the Ising, tricritical Ising and 3-state Potts models.Comment: 8 pages, no figure
Boundary field induced first-order transition in the 2D Ising model: numerical study
In a recent paper, Clusel and Fortin [J. Phys. A.: Math. Gen. 39 (2006) 995]
presented an analytical study of a first-order transition induced by an
inhomogeneous boundary magnetic field in the two-dimensional Ising model. They
identified the transition that separates the regime where the interface is
localized near the boundary from the one where it is propagating inside the
bulk. Inspired by these results, we measured the interface tension by using
multimagnetic simulations combined with parallel tempering to determine the
phase transition and the location of the interface. Our results are in very
good agreement with the theoretical predictions. Furthermore, we studied the
spin-spin correlation function for which no analytical results are available.Comment: 12 pages, 7 figures, 2 table
Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual
The three-dimensional purely plaquette gonihedric Ising model and its dual
are investigated to resolve inconsistencies in the literature for the values of
the inverse transition temperature of the very strong temperature-driven
first-order phase transition that is apparent in the system. Multicanonical
simulations of this model allow us to measure system configurations that are
suppressed by more than 60 orders of magnitude compared to probable states.
With the resulting high-precision data, we find excellent agreement with our
recently proposed nonstandard finite-size scaling laws for models with a
macroscopic degeneracy of the low-temperature phase by challenging the
prefactors numerically. We find an overall consistent inverse transition
temperature of 0.551334(8) from the simulations of the original model both with
periodic and fixed boundary conditions, and the dual model with periodic
boundary conditions. For the original model with periodic boundary conditions,
we obtain the first reliable estimate of the interface tension, 0.12037(18),
using the statistics of suppressed configurations
Macroscopic Degeneracy and order in the 3d plaquette Ising model
The purely plaquette 3d Ising Hamiltonian with the spins living at the
vertices of a cubic lattice displays several interesting features. The
symmetries of the model lead to a macroscopic degeneracy of the low-temperature
phase and prevent the definition of a standard magnetic order parameter.
Consideration of the strongly anisotropic limit of the model suggests that a
layered, "fuki-nuke" order still exists and we confirm this with multicanonical
simulations. The macroscopic degeneracy of the low-temperature phase also
changes the finite-size scaling corrections at the first-order transition in
the model and we see this must be taken into account when analysing our
measurements.Comment: arXiv admin note: text overlap with arXiv:1412.442
Multi-overlap simulations of spin glasses
We present results of recent high-statistics Monte Carlo simulations of the
Edwards-Anderson Ising spin-glass model in three and four dimensions. The study
is based on a non-Boltzmann sampling technique, the multi-overlap algorithm
which is specifically tailored for sampling rare-event states. We thus
concentrate on those properties which are difficult to obtain with standard
canonical Boltzmann sampling such as the free-energy barriers F^q_B in the
probability density P_J(q) of the Parisi overlap parameter q and the behaviour
of the tails of the disorder averaged density P(q) = [P_J(q)]_av.Comment: 14 pages, Latex, 18 Postscript figures, to be published in NIC Series
- Publication Series of the John von Neumann Institute for Computing (NIC
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
Exact solutions to plaquette Ising models with free and periodic boundaries
An anisotropic limit of the 3d plaquette Ising model, in which the plaquette
couplings in one direction were set to zero, was solved for free boundary
conditions by Suzuki (Phys. Rev. Lett. 28 (1972) 507), who later dubbed it the
fuki-nuke, or "no-ceiling", model. Defining new spin variables as the product
of nearest-neighbour spins transforms the Hamiltonian into that of a stack of
(standard) 2d Ising models and reveals the planar nature of the magnetic order,
which is also present in the fully isotropic 3d plaquette model. More recently,
the solution of the fuki-nuke model was discussed for periodic boundary
conditions, which require a different approach to defining the product spin
transformation, by Castelnovo et al. (Phys. Rev. B 81 (2010) 184303).
We clarify the exact relation between partition functions with free and
periodic boundary conditions expressed in terms of original and product spin
variables for the 2d plaquette and 3d fuki-nuke models, noting that the
differences are already present in the 1d Ising model. In addition, we solve
the 2d plaquette Ising model with helical boundary conditions. The various
exactly solved examples illustrate how correlations can be induced in finite
systems as a consequence of the choice of boundary conditions.Comment: v5 - The title is changed to better reflect the contents and the
exposition is streamlined. Version accepted for publicatio
Fluctuation Pressure of a Stack of Membranes
We calculate the universal pressure constants of a stack of N membranes
between walls by strong-coupling theory. The results are in very good agreement
with values from Monte-Carlo simulations.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/31
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