Quenched free energy in random matrix model

Abstract We compute the quenched free energy in the Gaussian random matrix model by directly evaluating the matrix integral without using the replica trick. We find that the quenched free energy is a monotonic function of the temperature and the entropy approaches log N at high temperature and vanishes at zero temperature.

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DISTRIBUTION FUNCTION FOR SHOT NOISE IN WIGNER-DYSON ENSEMBLES

International Journal of Modern Physics B ◽

10.1142/s0217979296000908 ◽

1996 ◽

Vol 10 (16) ◽

pp. 1999-2006 ◽

Cited By ~ 4

Author(s):

K.A. MUTTALIB ◽

Y. CHEN

Keyword(s):

Distribution Function ◽

Generating Function ◽

Matrix Model ◽

Shot Noise ◽

Random Matrix ◽

Zero Temperature ◽

Channel System ◽

Quantum Regime ◽

Random Matrix Model ◽

General Method

We obtain the generating function for shot noise through a random multi-channel system in the zero temperature quantum regime using a random matrix model. The generating function is a product statistic as opposed to a linear one, and we develop a general method to obtain fluctuation properties of such product statistics within a random matrix framework.

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A random matrix model with non-pairwise contracted indices

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptz057 ◽

2019 ◽

Vol 2019 (7) ◽

Cited By ~ 2

Author(s):

Luca Lionni ◽

Naoki Sasakura

Keyword(s):

Matrix Model ◽

Random Matrix ◽

Spherical Model ◽

Tensor Model ◽

Probabilistic Interpretation ◽

Random Matrix Model ◽

The Matrix ◽

Replicated Systems ◽

Random Tensor

Abstract We consider a random matrix model with both pairwise and non-pairwise contracted indices. The partition function of the matrix model is similar to that appearing in some replicated systems with random tensor couplings, such as the $p$-spin spherical model for the spin glass. We analyze the model using Feynman diagrammatic expansions, and provide an exhaustive characterization of the graphs that dominate when the dimensions of the pairwise and (or) non-pairwise contracted indices are large. We apply this to investigate the properties of the wave function of a toy model closely related to a tensor model in the Hamilton formalism, which is studied in a quantum gravity context, and obtain a result in favor of the consistency of the quantum probabilistic interpretation of this tensor model.

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TOPOLOGICAL SUSCEPTIBILITY AT FINITE TEMPERATURE IN A RANDOM MATRIX MODEL

Modern Physics Letters A ◽

10.1142/s0217732308029599 ◽

2008 ◽

Vol 23 (27n30) ◽

pp. 2465-2468 ◽

Cited By ~ 3

Author(s):

MUNEHISA OHTANI ◽

CHRISTOPH LEHNER ◽

TILO WETTIG ◽

TETSUO HATSUDA

Keyword(s):

Matrix Model ◽

Random Matrix ◽

Finite Temperature ◽

Chiral Condensate ◽

Zero Temperature ◽

Chiral Phase ◽

Modified Model ◽

Random Matrix Model ◽

Model Combining ◽

Quark Mass Dependence

The temperature and quark mass dependence of the topological susceptibility is analyzed in a random matrix model. A model combining random matrices and the lowest Matsubara frequency is known to describe the chiral phase transition of QCD qualitatively, but at finite temperature it suppresses the topological susceptibility in the thermodynamic limit by the inverse of the volume. We propose a modified model in which the topological susceptibility at finite temperature behaves reasonably. The modified model reproduces the chiral condensate and the zero-temperature result for the topological susceptibility of the conventional model, and it leads to a topological susceptibility at finite temperature in qualitative agreement with lattice QCD results.

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Quenched free energy from spacetime D-branes

Journal of High Energy Physics ◽

10.1007/jhep03(2021)073 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Kazumi Okuyama

Keyword(s):

Free Energy ◽

Integral Representation ◽

Generating Function ◽

Matrix Model ◽

Random Matrix ◽

Random Systems ◽

Random Matrix Model ◽

Monotonically Decreasing Function

Abstract We propose a useful integral representation of the quenched free energy which is applicable to any random systems. Our formula involves the generating function of multi-boundary correlators, which can be interpreted on the bulk gravity side as spacetime D-branes introduced by Marolf and Maxfield in [arXiv:2002.08950]. As an example, we apply our formalism to the Airy limit of the random matrix model and compute its quenched free energy under certain approximations of the generating function of correlators. It turns out that the resulting quenched free energy is a monotonically decreasing function of the temperature, as expected.

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MATRIX MODELS AND ONE-DIMENSIONAL OPEN STRING THEORY

International Journal of Modern Physics A ◽

10.1142/s0217751x93001466 ◽

1993 ◽

Vol 08 (20) ◽

pp. 3599-3614 ◽

Cited By ~ 9

Author(s):

JOSEPH A. MINAHAN

Keyword(s):

Free Energy ◽

String Theory ◽

Matrix Model ◽

Scaling Limit ◽

Open String ◽

Model Potential ◽

Boundary Field ◽

Random Matrix Model ◽

Open Strings ◽

The Matrix

We propose a random matrix model as a representation for D = 1 open strings. We show that the model with one flavor of boundary fields is equivalent to N fermions with spin in a central potential that also includes a long-range ferromagnetic interaction between the fermions that falls off as 1/(rij)2. We also generalize this theory to contain an arbitrary number of flavors. For an appropriate choice of the matrix model potential the ground state of the system can be found. Using this potential, we calculate the free energy in the double scaling limit and show that the free energy expansion has the expected form for a theory of open and closed strings if the boundary field mass and couplings have a logarithmic divergence. We then examine the critical properties of this theory and show that the length of the boundary around a hole remains finite, even near the critical point. We also argue that unlike critical string theory or a D = 0 theory, the open string coupling constant is a free parameter.

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Extremal correlators and random matrix theory

Journal of High Energy Physics ◽

10.1007/jhep04(2021)214 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Alba Grassi ◽

Zohar Komargodski ◽

Luigi Tizzano

Keyword(s):

Field Theory ◽

Gauge Theory ◽

Matrix Model ◽

Effective Field Theory ◽

Random Matrix ◽

Correlation Functions ◽

Matrix Theory ◽

Effective Field ◽

Random Matrix Model ◽

Large Charge

Abstract We study the correlation functions of Coulomb branch operators of four-dimensional $$ \mathcal{N} $$ N = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.

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