scholarly journals Charting the scaling region of the Ising universality class in two and three dimensions

2020 ◽  
Vol 102 (1) ◽  
Author(s):  
Michele Caselle ◽  
Marianna Sorba
Keyword(s):  
Universality Class ◽  
Three Dimensions ◽  
Scaling Region

scholarly journals Bootstrapping MN and tetragonal CFTs in three dimensions

2019 ◽  
Vol 7 (1) ◽  
Author(s):  
Andreas Stergiou
Keyword(s):  
Phase Transition ◽  
Rare Earth ◽  
Phase Transitions ◽  
Structural Phase ◽  
Earth Metal ◽  
Universality Class ◽  
Three Dimensions ◽  
Global Symmetry ◽  
Conformal Bootstrap ◽  
The Rare Earth

Conformal field theories (CFTs) with MN and tetragonal global symmetry in d=2+1d=2+1 dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions. As a result, they have been studied in great detail with the \varepsilon=4-dε=4−d expansion and other field theory methods. The study of these theories with the nonperturbative numerical conformal bootstrap is initiated in this work. Bounds for operator dimensions are obtained and they are found to possess sharp kinks in the MN case, suggesting the existence of full-fledged CFTs. Based on the existence of a certain large-NN expansion in theories with MN symmetry, these are argued to be the CFTs predicted by the \varepsilonε expansion. In the tetragonal case no new kinks are found, consistently with the absence of such CFTs in the \varepsilonε expansion. Estimates for critical exponents are provided for a few cases describing phase transitions in actual physical systems. In two particular MN cases, corresponding to theories with global symmetry groups O(2)^2\rtimes S_2O(2)2⋊S2 and O(2)^3\rtimes S_3O(2)3⋊S3, a second kink is found. In the O(2)^2\rtimes S_2O(2)2⋊S2 case it is argued to be saturated by a CFT that belongs to a new universality class relevant for the structural phase transition of NbO_22 and paramagnetic-helimagnetic transitions of the rare-earth metals Ho and Dy. In the O(2)^3\rtimes S_3O(2)3⋊S3 case it is suggested that the CFT that saturates the second kink belongs to a new universality class relevant for the paramagnetic-antiferromagnetic phase transition of the rare-earth metal Nd.

scholarly journals New universality class in three dimensions: The critical Blume-Capel model

2017 ◽  
Vol 96 (8) ◽  
Author(s):  
A. Codello ◽  
M. Safari ◽  
G. P. Vacca ◽  
O. Zanusso
Keyword(s):  
Universality Class ◽  
Three Dimensions

scholarly journals Wilsonian renormalization group in the functional non-perturbative approach

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040001
Author(s):  
Gian Paolo Vacca
Keyword(s):  
Renormalization Group ◽  
Proper Time ◽  
Functional Relation ◽  
Infinite Family ◽  
Coarse Graining ◽  
Universality Class ◽  
Three Dimensions ◽  
Derivative Expansion ◽  
Perturbative Approach ◽  
New Applications

We consider a functional relation between a given Wilsonian renormalization group (RG) flow, which has to be related to a specific coarse-graining procedure, and an infinite family of (UV cutoff) scale-dependent field redefinitions. Within this framework, one can define a family of Wilsonian proper-time (PT) exact RG equations associated to an arbitrary regulator function. New applications of these RG flow schemes to the Ising Universality class in three dimensions in the derivative expansion are shortly illustrated.

scholarly journals New universality class in three dimensions?: the antiferromagnetic RP2 model

1996 ◽  
Vol 378 (1-4) ◽  
pp. 207-212 ◽  
Author(s):  
H.G. Ballesteros ◽  
L.A. Fernández ◽  
V. Martín-Mayor ◽  
A. Muñoz Sudupe
Keyword(s):  
Universality Class ◽  
Three Dimensions

scholarly journals Kinetic Roughening of Interfaces in Driven Systems

1990 ◽  
Vol 205 ◽  
Author(s):  
Bruno Grossmann ◽  
Hong Guo ◽  
Martin Grant
Keyword(s):  
Finite Size ◽  
Universality Class ◽  
Discrete Models ◽  
Three Dimensions ◽  
Discrete Version ◽  
Scaling Analysis ◽  
Careful Study ◽  
Dynamical Scaling ◽  
Kinetic Roughening ◽  
Roughening Transition

We study the dynamics of an interface driven far from equilibrium in three dimensions. The relationship of the phenomena to self-organized critical phenomena is discussed. Numerical results are obtained for three models which simulate the growth of an interface: the Kardar-Parisi-Zhang equation, a discrete version of that model, and a solid-on-solid model with asymmetric rates of evaporation and condensation. We show that the three models belong to the same dynamical universality class by estimating the dynamical scaling exponents and the scaling functions. We confirm the results by a careful study of the crossover effects. In particular, we propose a crossover scaling ansatz and verify it numerically. Furthermore, the discrete models exhibit a kinetic roughening transition. We study this phenomenon by monitoring the surface step energy which shows a drastic jump at a finite temperature for a given driving force. At the same temperature, a finite size scaling analysis on the bond energy fluctuation shows a diverging peak [1].

scholarly journals TRICRITICAL ISING MODEL NEAR CRITICALITY

1998 ◽  
Vol 13 (07) ◽  
pp. 1145-1157 ◽  
Author(s):  
RICCARDO GUIDA
Keyword(s):  
Ising Model ◽  
Tricritical Point ◽  
Form Factors ◽  
Universality Class ◽  
Perturbative Expansion ◽  
Long Distance ◽  
Conformal Theory ◽  
Expansion Form ◽  
Scaling Region ◽  
Distance Behavior

The most relevant thermal perturbation of the continuous d=2 minimal conformal theory with c=7/10 (Tricritical Ising Model) is treated here. This model describes the scaling region of the ϕ6 universality class near the tricritical point. The problematic IR divergences of the naive perturbative expansion around conformal theories are dealt within the OPE approach developed at all orders by the authors. The main result is a description of the short distance behavior of correlators that is compared with existing long distance expansion (form factors approach) related to the integrability of the model.

High-resolution scanning electron microscopy (HRSEM) of mitochondria from various rat tissues

1988 ◽  
Vol 46 ◽  
pp. 14-15
Author(s):  
P.J. Lea ◽  
M.J. Hollenberg
Keyword(s):  
Electron Microscopy ◽  
Pigment Epithelium ◽  
Retinal Pigment ◽  
Rat Hepatocytes ◽  
Three Dimensions ◽  
Objective Lens ◽  
Rat Tissues ◽  
Thin Sections ◽  
Reconstruction Methods ◽  
Scanning Electron

Our current understanding of mitochondrial ultrastructure has been derived primarily from thin sections using transmission electron microscopy (TEM). This information has been extrapolated into three dimensions by artist's impressions (1) or serial sectioning techniques in combination with computer processing (2). The resolution of serial reconstruction methods is limited by section thickness whereas artist's impressions have obvious disadvantages.In contrast, the new techniques of HRSEM used in this study (3) offer the opportunity to view simultaneously both the internal and external structure of mitochondria directly in three dimensions and in detail.The tridimensional ultrastructure of mitochondria from rat hepatocytes, retinal (retinal pigment epithelium), renal (proximal convoluted tubule) and adrenal cortex cells were studied by HRSEM. The specimens were prepared by aldehyde-osmium fixation in combination with freeze cleavage followed by partial extraction of cytosol with a weak solution of osmium tetroxide (4). The specimens were examined with a Hitachi S-570 scanning electron microscope, resolution better than 30 nm, where the secondary electron detector is located in the column directly above the specimen inserted within the objective lens.

Inelastic Electron Scattering from Valence Electrons in Aluminum

1976 ◽  
Vol 34 ◽  
pp. 462-463
Author(s):  
P. E. Batson ◽  
C. H. Chen ◽  
J. Silcox
Keyword(s):  
Electron Scattering ◽  
Single Scattering ◽  
Three Dimensions ◽  
Inelastic Electron ◽  
Weak Beam ◽  
Scattering Spectrum ◽  
Valence Electrons ◽  
Diffraction Patterns ◽  
Electronic Scattering

We wish to report in this paper measurements of the inelastic scattering component due to the collective excitations (plasmons) and single particlehole excitations of the valence electrons in Al. Such scattering contributes to the diffuse electronic scattering seen in electron diffraction patterns and has recently been considered of significance in weak-beam images (see Gai and Howie) . A major problem in the determination of such scattering is the proper correction for multiple scattering. We outline here a procedure which we believe suitably deals with such problems and report the observed single scattering spectrum.In principle, one can use the procedure of Misell and Jones—suitably generalized to three dimensions (qx, qy and #x2206;E)--to derive single scattering profiles. However, such a computation becomes prohibitively large if applied in a brute force fashion since the quasi-elastic scattering (and associated multiple electronic scattering) extends to much larger angles than the multiple electronic scattering on its own.

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