930 research outputs found
Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems
We investigate the relation between spontaneous and explicit replica symmetry
breaking in the theory of disordered systems. On general ground, we prove the
equivalence between the replicon operator associated with the stability of the
replica symmetric solution in the standard replica scheme and the operator
signaling a breakdown of the solution with analytic field dependence in a
scheme in which replica symmetry is explicitly broken by applied sources. This
opens the possibility to study, via the recently developed functional
renormalization group, unresolved questions related to spontaneous replica
symmetry breaking and spin-glass behavior in finite-dimensional disordered
systems.Comment: 16 page
The full Schwinger-Dyson tower for random tensor models
We treat random rank- tensor models as -dimensional quantum field
theories---tensor field theories (TFT)---and review some of their
non-perturbative methods. We classify the correlation functions of complex
tensor field theories by boundary graphs, sketch the derivation of the
Ward-Takahashi identity and stress its relevance in the derivation of the tower
of exact, analytic Schwinger-Dyson equations for all the correlation functions
(with connected boundary) of TFTs with quartic pillow-like interactions.Comment: Proceedings: Corfu 2017 Training School "Quantum Spacetime and
Physics Models
SYK Model, Chaos and Conserved Charge
We study the SYK model with complex fermions, in the presence of an
all-to-all -body interaction, with a non-vanishing chemical potential. We
find that, in the large limit, this model can be solved exactly and the
corresponding Lyapunov exponent can be obtained semi-analytically. The
resulting Lyapunov exponent is a sensitive function of the chemical potential
. Even when the coupling , which corresponds to the disorder averaged
values of the all to all fermion interaction, is large, values of which
are exponentially small compared to lead to suppression of the Lyapunov
exponent.Comment: 18pages, 4 figures, v2:references and acknowledgment added, typos
correcte
Coarsening of Disordered Quantum Rotors under a Bias Voltage
We solve the dynamics of an ensemble of interacting rotors coupled to two
leads at different chemical potential letting a current flow through the system
and driving it out of equilibrium. We show that at low temperature the
coarsening phase persists under the voltage drop up to a critical value of the
applied potential that depends on the characteristics of the electron
reservoirs. We discuss the properties of the critical surface in the
temperature, voltage, strength of quantum fluctuations and coupling to the bath
phase diagram. We analyze the coarsening regime finding, in particular, which
features are essentially quantum mechanical and which are basically classical
in nature. We demonstrate that the system evolves via the growth of a coherence
length with the same time-dependence as in the classical limit, -- the scalar curvature driven universality class. We obtain the
scaling function of the correlation function at late epochs in the coarsening
regime and we prove that it coincides with the classical one once a prefactor
that encodes the dependence on all the parameters is factorized. We derive a
generic formula for the current flowing through the system and we show that,
for this model, it rapidly approaches a constant that we compute.Comment: 53 pages, 12 figure
A Supersymmetric SYK-like Tensor Model
We consider a supersymmetric SYK-like model without quenched disorder that is
built by coupling two kinds of fermionic N=1 tensor-valued superfields,
"quarks" and "mesons". We prove that the model has a well-defined large-N limit
in which the (s)quark 2-point functions are dominated by mesonic "melon"
diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and
show that in the IR, the solution agrees with that of the supersymmetric SYK
model.Comment: 29 pages, 19 figures. v2: 3 references and more details of the
computation in section 3.1 are adde
Schwinger-Dyson equations and disorder
Using simple models in D=0+0 and D=0+1 dimensions we construct partition
functions and compute two-point correlations. The exact result is compared with
saddle-point approximation and solutions of Schwinger-Dyson equations. When
integrals are dominated by more than one saddle-point we find Schwinger-Dyson
equations do not reproduce the correct results unless the action is first
transformed into dual variables.Comment: 7 pages, 6 figure
Uncolored Random Tensors, Melon Diagrams, and the SYK Models
Certain models with rank- tensor degrees of freedom have been shown by
Gurau and collaborators to possess a novel large limit, where is
held fixed. In this limit the perturbative expansion in the quartic coupling
constant, , is dominated by a special class of "melon" diagrams. We study
"uncolored" models of this type, which contain a single copy of real rank-
tensor. Its three indexes are distinguishable; therefore, the models possess
symmetry with the tensor field transforming in the tri-fundamental
representation. Such uncolored models also possess the large limit
dominated by the melon diagrams. The quantum mechanics of a real anti-commuting
tensor therefore has a similar large limit to the model recently introduced
by Witten as an implementation of the Sachdev-Ye-Kitaev (SYK) model which does
not require disorder. Gauging the symmetry in our quantum mechanical
model removes the non-singlet states; therefore, one can search for its
well-defined gravity dual. We point out, however, that the model possesses a
vast number of gauge-invariant operators involving higher powers of the tensor
field, suggesting that the complete gravity dual will be intricate. We also
discuss the quantum mechanics of a complex 3-index anti-commuting tensor, which
has symmetry and argue that it is equivalent in the large
limit to a version of SYK model with complex fermions. Finally, we discuss
similar models of a commuting tensor in dimension . While the quartic
interaction is not positive definite, we construct the large
Schwinger-Dyson equation for the two-point function and show that its solution
is consistent with conformal invariance. We carry out a perturbative check of
this result using the expansion.Comment: 26 pages, 16 figures, v2: sections 3 and 5 expanded, minor
corrections, references added, v3: minor corrections, a reference added, v4:
minor corrections, v5: spectrum of the complex model corrected; a note added
about "uncolored" higher rank tensor
A geometric approach to free variable loop equations in discretized theories of 2D gravity
We present a self-contained analysis of theories of discrete 2D gravity
coupled to matter, using geometric methods to derive equations for generating
functions in terms of free (noncommuting) variables. For the class of discrete
gravity theories which correspond to matrix models, our method is a
generalization of the technique of Schwinger-Dyson equations and is closely
related to recent work describing the master field in terms of noncommuting
variables; the important differences are that we derive a single equation for
the generating function using purely graphical arguments, and that the approach
is applicable to a broader class of theories than those described by matrix
models. Several example applications are given here, including theories of
gravity coupled to a single Ising spin (), multiple Ising spins (), a general class of two-matrix models which includes the Ising theory and
its dual, the three-state Potts model, and a dually weighted graph model which
does not admit a simple description in terms of matrix models.Comment: 40 pages, 8 figures, LaTeX; final publication versio
Phase diagram and fixed points of tensorial Gross-Neveu models in three dimensions
Perturbing the standard Gross-Neveu model for fermions by quartic
interactions with the appropriate tensorial contraction patterns, we reduce the
original symmetry to either or . In the large- limit, we show that in three dimensions such
models admit new ultraviolet fixed points with reduced symmetry, besides the
well-known one with maximal symmetry. The phase diagram notably presents a new
phase with spontaneous symmetry breaking of one component of the
symmetry group.Comment: 31 pages, 9 figure
Duality in Long-Range Ising Ferromagnets
It is proved that for a system of spins having an
interaction energy with all the
strictly positive,one can construct a dual formulation by associating a dual
spin to each triplet of distinct sites and . The
dual interaction energy reads with , and it is invariant under
local symmetries. We discuss the gauge-fixing procedure, identities relating
averages of order and disorder variables and representations of various
quantities as integrals over Grassmann variables. The relevance of these
results for Polyakov's approach of the 3D Ising model is briefly discussed.Comment: 16 pp., UIOWA-91-2
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