Normal Form for Renormalization Groups

Raju, Archishman; Clement, Colin B.; Hayden, Lorien X.; Kent-Dobias, Jaron; Liarte, Danilo B.; Rocklin, D. Zeb; Sethna, James P.

doi:10.1103/physrevx.9.021014

Cited by 19 publications

(17 citation statements)

References 88 publications

(101 reference statements)

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“…in the bosonic and in the fermionic theory, respectively. Non-local generalizations of bosonic vector models were also considered in [2,[10][11][12] with the difference that the non-locality resides in the kinetic term of the vector fields rather than in their quartic interaction. Similar strong/weak dualities were also found in [13,14] for purely three-dimensional RG flows involving couplings between multiple vector models.…”

Section: Introductionmentioning

confidence: 99%

3d large $N$ vector models at the boundary

2021

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We consider a 4d scalar field coupled to large NN free or critical O(N)O(N) vector models, either bosonic or fermionic, on a 3d boundary. We compute the \betaβ function of the classically marginal bulk/boundary interaction at the first non-trivial order in the large NN expansion and exactly in the coupling. Starting with the free (critical) vector model at weak coupling, we find a fixed point at infinite coupling in which the boundary theory is the critical (free) vector model and the bulk decouples. We show that a strong/weak duality relates one description of the renormalization group flow to another one in which the free and the critical vector models are exchanged. We then consider the theory with an additional Maxwell field in the bulk, which also gives decoupling limits with gauged vector models on the boundary.

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Section: Introductionmentioning

confidence: 99%

3d large $N$ vector models at the boundary

2021

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“…These power laws are often universal for a large variety of microscopically different systems [1], which only share the presence of a symmetry breaking transition and the specific symmetry of the order parameter. The existence of universality within the theory of critical phenomena was clarified several decades ago, thanks to the analogy between the thermodynamic limit of many body systems and the long-time behaviour of dynamical systems that was established by the renormalization group (RG) approach [2]. This success is exemplified by the study of phase transitions and spontaneous symmetry breaking in the paradigmatic O(n) symmetric vector model [3].…”

Section: Introductionmentioning

confidence: 99%

“…. Critical exponents of the Ising model as a function of d ∈[2,4] from dimensional regularization (DR)[89], conformal bootstrap (CB)[4,90,91] and functional renormalization group (FRG)[5,6].…”

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confidence: 99%

Complex networks with tuneable dimensions as a universality playground

Millán,

Gori,

Battiston

et al. 2020

Preprint

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Universality is one of the key concepts in understanding critical phenomena. However, for interacting inhomogeneous systems described by complex networks a clear understanding of the relevant parameters for universality is still missing. Here we discuss the role of a fundamental network parameter, the spectral dimension, neglected in previous investigations. For this purpose, we construct a complex network model where the probability of a bond between two nodes is proportional to a power law of the nodes' distances. By explicit computation we prove that the spectral dimension for this model can be tuned continuously from 1 to infinity, and we discuss related network connectivity measures. We propose our model as a tool to probe universal behaviour on inhomogeneous structures and comment on the possibility that the universal behaviour of correlated models on such networks mimics the one of continuous field theories in fractional euclidean dimensions. We suggest that similar structures could be engineered in atomic, molecular and optical devices in order to tune universal properties to a desired value.

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“…Because of the peculiar nature of the scaling at a lower critical dimension, a proper finite-size scaling analysis requires very large system sizes, as, e.g., in studies of the RFIM in d = 2 for which sizes of 10 6 or more spins have been considered (see Refs [90][91][92]…”

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confidence: 99%

Statistical mechanics of coupled supercooled liquids in finite dimensions

Guiselin

Tarjus

2022

SciPost Phys.

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We study the statistical mechanics of supercooled liquids when the system evolves at a temperature TT with a field \epsilonϵ linearly coupled to its overlap with a reference configuration of the same liquid sampled at a temperature T_0T0. We use mean-field theory to fully characterize the influence of the reference temperature T_0T0, and we mainly study the case of a fixed, low-T_0T0 value in computer simulations. We numerically investigate the extended phase diagram in the (\epsilon,T)(ϵ,T) plane of model glass-forming liquids in spatial dimensions d=2d=2 and d=3d=3, relying on umbrella sampling and reweighting techniques. For both 2d2d and 3d3d cases, a similar phenomenology with nontrivial thermodynamic fluctuations of the overlap is observed at low temperatures, but a detailed finite-size analysis reveals qualitatively distinct behaviors. We establish the existence of a first-order transition line for nonzero \epsilonϵ ending in a critical point in the universality class of the random-field Ising model (RFIM) in d=3d=3. In d=2d=2 instead, no phase transition is found in large enough systems at least down to temperatures below the extrapolated calorimetric glass transition temperature T_gTg. Our results confirm that glass-forming liquid samples of limited size display the thermodynamic fluctuations expected for finite systems undergoing a random first-order transition. They also support the relevance of the physics of the RFIM for supercooled liquids, which may then explain the qualitative difference between 2d2d and 3d3d glass-formers.

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Normal Form for Renormalization Groups

Cited by 19 publications

References 88 publications

3d large $N$ vector models at the boundary

3d large $N$ vector models at the boundary

Complex networks with tuneable dimensions as a universality playground

Statistical mechanics of coupled supercooled liquids in finite dimensions

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