Symmetry classification of continuous phase transitions in two dimensions

1981 ◽  
Vol 24 (3) ◽  
pp. 1482-1492 ◽  
Author(s):  
Craig Rottman
Keyword(s):  
Phase Transitions ◽  
Continuous Phase ◽  
Two Dimensions ◽  
Symmetry Classification

scholarly journals Fermi surface reconstruction and multiple quantum phase transitions in the antiferromagnet CeRhIn5

2015 ◽  
Vol 112 (3) ◽  
pp. 673-678 ◽  
Author(s):  
Lin Jiao ◽  
Ye Chen ◽  
Yoshimitsu Kohama ◽  
David Graf ◽  
E. D. Bauer ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Fermi Surface ◽  
Quantum Phase Transitions ◽  
Continuous Phase ◽  
Multiple Quantum ◽  
Quantum Critical Points ◽  
Thermally Driven ◽  
Significant Step ◽  
Open Issues

Conventional, thermally driven continuous phase transitions are described by universal critical behavior that is independent of the specific microscopic details of a material. However, many current studies focus on materials that exhibit quantum-driven continuous phase transitions (quantum critical points, or QCPs) at absolute zero temperature. The classification of such QCPs and the question of whether they show universal behavior remain open issues. Here we report measurements of heat capacity and de Haas–van Alphen (dHvA) oscillations at low temperatures across a field-induced antiferromagnetic QCP (Bc0 ≈ 50 T) in the heavy-fermion metal CeRhIn5. A sharp, magnetic-field-induced change in Fermi surface is detected both in the dHvA effect and Hall resistivity at B0* ≈ 30 T, well inside the antiferromagnetic phase. Comparisons with band-structure calculations and properties of isostructural CeCoIn5 suggest that the Fermi-surface change at B0* is associated with a localized-to-itinerant transition of the Ce-4f electrons in CeRhIn5. Taken in conjunction with pressure experiments, our results demonstrate that at least two distinct classes of QCP are observable in CeRhIn5, a significant step toward the derivation of a universal phase diagram for QCPs.

Classification of continuous phase transitions and stable phases. I. Six-dimensional order parameters

1986 ◽  
Vol 33 (3) ◽  
pp. 1774-1788 ◽  
Author(s):  
Jai Sam Kim ◽  
Dorian M. Hatch ◽  
Harold T. Stokes
Keyword(s):  
Phase Transitions ◽  
Continuous Phase ◽  
Order Parameters

scholarly journals Monotone Cellular Automata in a Random Environment

2015 ◽  
Vol 24 (4) ◽  
pp. 687-722 ◽  
Author(s):  
BÉLA BOLLOBÁS ◽  
PAUL SMITH ◽  
ANDREW UZZELL
Keyword(s):  
Phase Transitions ◽  
Cellular Automata ◽  
Two Dimensions ◽  
Bootstrap Percolation ◽  
Unified Theory ◽  
Critical Probability ◽  
The Family ◽  
Update Rules ◽  
Critical Class

In this paper we study in complete generality the family of two-state, deterministic, monotone, local, homogeneous cellular automata in $\mathbb{Z}$d with random initial configurations. Formally, we are given a set $\mathcal{U}$ = {X1,. . . , Xm} of finite subsets of $\mathbb{Z}$d \ {0}, and an initial set A0 ⊂ $\mathbb{Z}$d of ‘infected’ sites, which we take to be random according to the product measure with density p. At time t ∈ $\mathbb{N}$, the set of infected sites At is the union of At-1 and the set of all x ∈ $\mathbb{Z}$d such that x + X ∈ At-1 for some X ∈ $\mathcal{U}$. Our model may alternatively be thought of as bootstrap percolation on $\mathbb{Z}$d with arbitrary update rules, and for this reason we call it $\mathcal{U}$-bootstrap percolation.In two dimensions, we give a classification of $\mathcal{U}$-bootstrap percolation models into three classes – supercritical, critical and subcritical – and we prove results about the phase transitions of all models belonging to the first two of these classes. More precisely, we show that the critical probability for percolation on ($\mathbb{Z}$/n$\mathbb{Z}$)2 is (log n)−Θ(1) for all models in the critical class, and that it is n−Θ(1) for all models in the supercritical class.The results in this paper are the first of any kind on bootstrap percolation considered in this level of generality, and in particular they are the first that make no assumptions of symmetry. It is the hope of the authors that this work will initiate a new, unified theory of bootstrap percolation on $\mathbb{Z}$d.

Classification of continuous phase transitions and stable phases. II. Four-dimensional order parameters

1986 ◽  
Vol 33 (9) ◽  
pp. 6210-6230 ◽  
Author(s):  
Jai Sam Kim ◽  
Harold T. Stokes ◽  
Dorian M. Hatch
Keyword(s):  
Phase Transitions ◽  
Continuous Phase ◽  
Order Parameters

Phase transitions in the six‐state vector Potts model in two dimensions

1984 ◽  
Vol 55 (6) ◽  
pp. 2429-2431 ◽  
Author(s):  
Challa S. S. Murty ◽  
D. P. Landau
Keyword(s):  
Phase Transitions ◽  
Potts Model ◽  
State Vector ◽  
Two Dimensions
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