25 research outputs found
The Information Geometry of the Ising Model on Planar Random Graphs
It has been suggested that an information geometric view of statistical
mechanics in which a metric is introduced onto the space of parameters provides
an interesting alternative characterisation of the phase structure,
particularly in the case where there are two such parameters -- such as the
Ising model with inverse temperature and external field .
In various two parameter calculable models the scalar curvature of
the information metric has been found to diverge at the phase transition point
and a plausible scaling relation postulated: . For spin models the necessity of calculating in
non-zero field has limited analytic consideration to 1D, mean-field and Bethe
lattice Ising models. In this letter we use the solution in field of the Ising
model on an ensemble of planar random graphs (where ) to evaluate the scaling behaviour of the scalar curvature, and find
. The apparent discrepancy is traced
back to the effect of a negative .Comment: Version accepted for publication in PRE, revtex
The Information Geometry of the Spherical Model
Motivated by previous observations that geometrizing statistical mechanics
offers an interesting alternative to more standard approaches,we have recently
calculated the curvature (the fundamental object in this approach) of the
information geometry metric for the Ising model on an ensemble of planar random
graphs. The standard critical exponents for this model are alpha=-1, beta=1/2,
gamma=2 and we found that the scalar curvature, R, behaves as
epsilon^(-2),where epsilon = beta_c - beta is the distance from criticality.
This contrasts with the naively expected R ~ epsilon^(-3) and the apparent
discrepancy was traced back to the effect of a negative alpha on the scaling of
R.
Oddly,the set of standard critical exponents is shared with the 3D spherical
model. In this paper we calculate the scaling behaviour of R for the 3D
spherical model, again finding that R ~ epsilon^(-2), coinciding with the
scaling behaviour of the Ising model on planar random graphs. We also discuss
briefly the scaling of R in higher dimensions, where mean-field behaviour sets
in.Comment: 7 pages, no figure
On the Thermodynamic Geometry and Critical Phenomena of AdS Black Holes
In this paper, we study various aspects of the equilibrium thermodynamic
state space geometry of AdS black holes. We first examine the
Reissner-Nordstrom-AdS (RN-AdS) and the Kerr-AdS black holes. In this context,
the state space scalar curvature of these black holes is analysed in various
regions of their thermodynamic parameter space. This provides important new
insights into the structure and significance of the scalar curvature. We
further investigate critical phenomena, and the behaviour of the scalar
curvature near criticality, for KN-AdS black holes in two mixed ensembles,
introduced and elucidated in our earlier work arXiv:1002.2538 [hep-th]. The
critical exponents are identical to those in the RN-AdS and Kerr-AdS cases in
the canonical ensemble. This suggests an universality in the scaling behaviour
near critical points of AdS black holes. Our results further highlight
qualitative differences in the thermodynamic state space geometry for electric
charge and angular momentum fluctuations of these.Comment: 1 + 37 Pages, LaTeX, includes 31 figures. A figure and a
clarification added
Thermodynamic Geometry of black hole in the deformed Horava-Lifshitz gravity
We investigate the thermodynamic geometry and phase transition of
Kehagias-Sfetsos black hole in the deformed Horava-Lifshitz gravity with
coupling constant . The phase transition in black hole
thermodynamics is thought to be associated with the divergence of the
capacities. And the structures of these divergent points are studied. We also
find that the thermodynamic curvature produced by the Ruppeiner metric is
positive definite for all and is divergence at
corresponded to the divergent points of and . These results
suggest that the microstructure of the black hole has an effective repulsive
interaction, which is very similar to the ideal gas of fermions. These may
shine some light on the microstructure of the black hole.Comment: 5 pages, 3 figure
Information Metric on Instanton Moduli Spaces in Nonlinear Sigma Models
We study the information metric on instanton moduli spaces in two-dimensional
nonlinear sigma models. In the CP^1 model, the information metric on the moduli
space of one instanton with the topological charge Q=k which is any positive
integer is a three-dimensional hyperbolic metric, which corresponds to
Euclidean anti--de Sitter space-time metric in three dimensions, and the
overall scale factor of the information metric is (4k^2)/3; this means that the
sectional curvature is -3/(4k^2). We also calculate the information metric in
the CP^2 model.Comment: 9 pages, LaTeX; added references for section 1; typos adde
Thermodynamic Geometry and Phase Transitions in Kerr-Newman-AdS Black Holes
We investigate phase transitions and critical phenomena in Kerr-Newman-Anti
de Sitter black holes in the framework of the geometry of their equilibrium
thermodynamic state space. The scalar curvature of these state space Riemannian
geometries is computed in various ensembles. The scalar curvature diverges at
the critical point of second order phase transitions for these systems.
Remarkably, however, we show that the state space scalar curvature also carries
information about the liquid-gas like first order phase transitions and the
consequent instabilities and phase coexistence for these black holes. This is
encoded in the turning point behavior and the multi-valued branched structure
of the scalar curvature in the neighborhood of these first order phase
transitions. We re-examine this first for the conventional Van der Waals
system, as a preliminary exercise. Subsequently, we study the Kerr-Newman-AdS
black holes for a grand canonical and two "mixed" ensembles and establish novel
phase structures. The state space scalar curvature bears out our assertion for
the first order phase transitions for both the known and the new phase
structures, and closely resembles the Van der Waals system.Comment: 1 + 41 pages, LaTeX, 46 figures. Discussions, clarifications and
references adde
Thermodynamic curvature and black holes
I give a relatively broad survey of thermodynamic curvature , one spanning
results in fluids and solids, spin systems, and black hole thermodynamics.
results from the thermodynamic information metric giving thermodynamic
fluctuations. has a unique status in thermodynamics as being a geometric
invariant, the same for any given thermodynamic state. In fluid and solid
systems, the sign of indicates the character of microscopic interactions,
repulsive or attractive. gives the average size of organized mesoscopic
fluctuating structures. The broad generality of thermodynamic principles might
lead one to believe the same for black hole thermodynamics. This paper explores
this issue with a systematic tabulation of results in a number of cases.Comment: 27 pages, 10 figures, 7 tables, 78 references. Talk presented at the
conference Breaking of Supersymmetry and Ultraviolet Divergences in extended
Supergravity, in Frascati, Italy, March 27, 2013. v2 corrects some small
problem
Propagation of leather leaf Chamaedaphne calyculata (L.) Moench from seeds and shoot cuttings
Flowering and fruit setting was analyzed in specimens of Chamedaphne calyculata (L.) Moench growing in a natural stand in the “Sicienko” reserve in the Drawa National Park. Seed production, seed viability and shoot rooting was investigated. It was shown that Chamaedaphne calyculata has abundant flowers but sets few fruits. Numerous seeds (even up to 87) were found in fruits; however, the percentage of developed seeds was low and ranged from 17% to 45%. The viability of developed seeds was similarly low (maximum 29%). The performed germination test showed a positive effect of stratification on the breaking of seed dormancy. Obtaining seedlings from seeds sown in vitro on agar medium was a considerable success. Shoots cut perpendicularly to the shoot axis, with a 1-cm incision on the side and treated with a rooting agent, rooted 100%. Shoots which were not treated with a rooting agent, irrespective of their having been incised or not, rooted 78%