scholarly journals Fermionic criticality of anisotropic nodal point semimetals away from the upper critical dimension: Exact exponents to leading order in 1Nf

2020 ◽  
Vol 2 (4) ◽  
Author(s):  
Mikolaj D. Uryszek ◽  
Frank Krüger ◽  
Elliot Christou
Keyword(s):  
Nodal Point ◽  
Critical Dimension ◽  
Leading Order ◽  
Upper Critical Dimension

scholarly journals Topological excitations in statistical field theory at the upper critical dimension

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Marco Panero ◽  
Antonio Smecca
Keyword(s):  
Field Theory ◽  
Monte Carlo Study ◽  
Critical Dimension ◽  
Density Profiles ◽  
Upper Critical Dimension ◽  
Four Dimensions ◽  
Topological Excitations ◽  
Classical Heisenberg Model ◽  
Statistical Field ◽  
Statistical Field Theory

Abstract We present a high-precision Monte Carlo study of the classical Heisenberg model in four dimensions. We investigate the properties of monopole-like topological excitations that are enforced in the broken-symmetry phase by imposing suitable boundary conditions. We show that the corresponding magnetization and energy-density profiles are accurately predicted by previous analytical calculations derived in quantum field theory, while the scaling of the low-energy parameters of this description questions an interpretation in terms of particle excitations. We discuss the relevance of these findings and their possible experimental applications in condensed-matter physics.

scholarly journals Power-law bounds for critical long-range percolation below the upper-critical dimension

2021 ◽  
Author(s):  
Tom Hutchcroft
Keyword(s):  
Long Range ◽  
Power Law ◽  
Upper Bound ◽  
Mean Field ◽  
Maximum Size ◽  
Finite Graph ◽  
Critical Dimension ◽  
Point Function ◽  
Upper Critical Dimension ◽  
Infinite Cluster

AbstractWe study long-range Bernoulli percolation on $${\mathbb {Z}}^d$$ Z d in which each two vertices x and y are connected by an edge with probability $$1-\exp (-\beta \Vert x-y\Vert ^{-d-\alpha })$$ 1 - exp ( - β ‖ x - y ‖ - d - α ) . It is a theorem of Noam Berger (Commun. Math. Phys., 2002) that if $$0<\alpha <d$$ 0 < α < d then there is no infinite cluster at the critical parameter $$\beta _c$$ β c . We give a new, quantitative proof of this theorem establishing the power-law upper bound $$\begin{aligned} {\mathbf {P}}_{\beta _c}\bigl (|K|\ge n\bigr ) \le C n^{-(d-\alpha )/(2d+\alpha )} \end{aligned}$$ P β c ( | K | ≥ n ) ≤ C n - ( d - α ) / ( 2 d + α ) for every $$n\ge 1$$ n ≥ 1 , where K is the cluster of the origin. We believe that this is the first rigorous power-law upper bound for a Bernoulli percolation model that is neither planar nor expected to exhibit mean-field critical behaviour. As part of the proof, we establish a universal inequality implying that the maximum size of a cluster in percolation on any finite graph is of the same order as its mean with high probability. We apply this inequality to derive a new rigorous hyperscaling inequality $$(2-\eta )(\delta +1)\le d(\delta -1)$$ ( 2 - η ) ( δ + 1 ) ≤ d ( δ - 1 ) relating the cluster-volume exponent $$\delta $$ δ and two-point function exponent $$\eta $$ η .

Chaotic spin glasses: An upper critical dimension (invited)

1984 ◽  
Vol 55 (6) ◽  
pp. 1646-1648 ◽  
Author(s):  
Susan R. McKay ◽  
A. Nihat Berker
Keyword(s):  
Spin Glasses ◽  
Critical Dimension ◽  
Upper Critical Dimension

scholarly journals Extra investigation of the self-organized critical Manna model at higher critical dimension

2021 ◽  
pp. 1-12
Author(s):  
Andrey Viktorovich Podlazov
Keyword(s):  
Power Law ◽  
Critical Dimension ◽  
The Self ◽  
Two Dimensional ◽  
Upper Critical Dimension ◽  
Self Organized ◽  
Logarithmic Corrections ◽  
Universal Indicator ◽  
Sandpile Models ◽  
Power Law Distributions

I investigate the nature of the upper critical dimension for isotropic conservative sandpile models and calculate the emerging logarithmic corrections to power-law distributions. I check the results experimentally using the case of Manna model with the theoretical solution known for all statement starting from the two-dimensional one. In addition, based on this solution, I construct a non-trivial super-universal indicator for this model. It characterizes the distribution of avalanches by time the border of their region needs to pass its width.

scholarly journals Scaling above the upper critical dimension in Ising models

1996 ◽  
Vol 54 (6) ◽  
pp. R3698-R3701 ◽  
Author(s):  
Giorgio Parisi ◽  
Juan J. Ruiz-Lorenzo
Keyword(s):  
Critical Dimension ◽  
Ising Models ◽  
Upper Critical Dimension
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