Geometric critical exponents in classical and quantum phase transitions

Kumar, Prashant; Sarkar, Tapobrata

doi:10.1103/physreve.90.042145

Cited by 27 publications

(40 citation statements)

References 20 publications

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“…This result agrees with that obtained in [18] for the van der Waals fluid. The third condition of the previous section is also satisfied.…”

Section: A Geometric Scaling Relation For Rn-ads Fluidssupporting

confidence: 92%

“…This result is strictly valid close to criticality, and is an example of a geometric scaling. In [18], it was argued from generic grounds that this relation should in general be true for two dimensional parameter manifolds, and we see that it is indeed the case here.…”

Section: A Geometric Scaling Relation For Rn-ads Fluidssupporting

confidence: 70%

“…In [18], it was pointed out that there are important relations between scalar quantities on the parameter manifold of classical and quantum systems, near criticality. In particular, it is natural to express scaling invariants in terms such scalar quantities.…”

Section: A Geometric Scaling Relation For Rn-ads Fluidsmentioning

confidence: 99%

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The geometry of RN-AdS fluids

Bairagya

Pal

et al. 2020

Physics Letters B

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We establish the parameter space geometry of a fluid system characterized by two constants, whose equation of state mimics that of the RN-AdS black hole. We call this the RN-AdS fluid. We study the scalar curvature on the parameter space of this system, and show its equivalence with the RN-AdS black hole, in the limit of vanishing specific heat at constant volume. Further, an analytical construction of the Widom line is established. We also numerically study the behavior of geodesics on the parameter space of the fluid, and find a geometric scaling relation near its second order critical point. *

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“…This result agrees with that obtained in [18] for the van der Waals fluid. The third condition of the previous section is also satisfied.…”

Section: A Geometric Scaling Relation For Rn-ads Fluidssupporting

confidence: 92%

Section: A Geometric Scaling Relation For Rn-ads Fluidssupporting

confidence: 70%

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The geometry of RN-AdS fluids

Bairagya

Pal

et al. 2020

Physics Letters B

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“…By computing JLC vector fields for the previous three and two dimensional Gaussian models in the Eqs. (113) and (115), we arrive at the following asymptotic relation…”

Section: B Complexitymentioning

confidence: 99%

Information geometric methods for complexity

Felice

Cafaro

Mancini

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and, whenever available, quantum physical settings. A paradigmatic example of a dramatic change in complexity is given by phase transitions (PTs). Hence, we review both global and local aspects of PTs described in terms of the scalar curvature of the parameter manifold and the components of the metric tensor, respectively. We also report on the behavior of geodesic paths on the parameter manifold used to gain insight into the dynamics of PTs. Going further, we survey measures of complexity arising in the geometric framework. In particular, we quantify complexity of networks in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. We are also concerned with complexity measures that account for the interactions of a given number of parts of a system that cannot be described in terms of a smaller number of parts of the system. Finally, we investigate complexity measures of entropic motion on curved statistical manifolds that arise from a probabilistic description of physical systems in the presence of limited information. The Kullback-Leibler divergence, the distance to an exponential family and volumes of curved parameter manifolds, are examples of essential IG notions exploited in our discussion of complexity. We conclude by discussing strengths, limits, and possible future applications of IG methods to the physics of complexity.

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“…To a somewhat lesser extent, same can be said about such connections found in thermodynamics of phase transitions ('Fisher-Ruppeiner metric') [110][111][112][113], quantum information and tensor network states [114][115][116][117][118][119][120], QHE hydrodynamics ('Fubini-Study metric') [121][122][123], Chern classes of the Bloch eigenstates of momentum [124][125][126], Berry phase of the adiabatic time evolution [127][128][129], etc. In all these different contexts, some underlying invariance under pertinent diffeomorphisms facilitates an elegant and insightful gravitational description.…”

Section: Emergent Geometry and 'Holography Light'mentioning

confidence: 99%

Demystifying the holographic mystique: A critical review

Khveshchenko¹

2016

Lith. J. Phys.

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Thus far, in spite of many interesting developments, the overall progress towards a systematic study and classification of various 'strange' metallic states of matter has been rather limited. To that end, it was argued that a recent proliferation of the ideas of holographic correspondence originating from string theory might offer a possible way out of the stalemate. However, after almost a decade of intensive studies into the proposed extensions of the holographic conjecture to a variety of condensed matter problems, the validity of this intriguing approach remains largely unknown. This discussion aims at ascertaining its true status and elucidating the conditions under which some of its predictions may indeed be right (albeit, possibly, for a wrong reason).Keywords: strongly correlated systems, holographic correspondence, transport theory, strange metals, analogue gravity PACS: 71.27.+a Condensed matter holography: the promiseAmong the outstanding grand problems in condensed matter physics is that of a deeper understanding and classification of the so-called 'strange metals' or compressible non-Fermi liquid (NFL) states of the strongly interacting systems. However, despite all the effort and a plethora of the important and nontrivial results obtained with the use of the traditional techniques, this program still remains far from completion.As an alternate approach, over the past decade there have been numerous attempts inspired by the hypothetical idea of holographic correspondence which originated from string/gravity/high energy theory (where it is known under the acronym AdS/ CFT) to adapt its main concepts to various condensed matter (or, even more generally, quantum manybody) systems at finite densities and temperatures [1][2][3][4][5][6][7].In its original context, the bona fide holographic principle postulates that certain d + 1-dimensional ('boundary') quantum field theories (e. g. the maximally supersymmetric SU(N) gauge theory) may allow for a dual description in terms of a string theory which, upon a proper compactification, amounts to a certain d + 2-dimensional ('bulk') supergravity. Moreover, in the strong coupling limit (characterized in terms of the t'Hooft coupling constant λ = g 2 N >> 1) and for a large rank N > > 1 of the gauge symmetry group, the bulk description can be further reduced down to a weakly fluctuating gravity model which can even be treated semiclassically at the lowest (0th) order of the underlying 1/N-expansion.In the practical applications of the holographic conjecture, the partition function of a strongly interacting boundary theory with the Lagrangian L(ϕ a ) would then be approximated by a saddle-point (classical) value of the bulk action described by the Lagrangian L(g μν ,…) which includes gravity and other fields dual to their boundary counterparts [1][2][3][4][5][6][7][8] (1) evaluated with the use of a fixed background metric ,while any quantum corrections would usually be neglected by invoking the small parameter 1/N.

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Geometric critical exponents in classical and quantum phase transitions

Cited by 27 publications

References 20 publications

The geometry of RN-AdS fluids

The geometry of RN-AdS fluids

Information geometric methods for complexity

Demystifying the holographic mystique: A critical review

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