Critical
Phenomena |

**In General** > s.a. complexity;
correlations [length]; renormalization
group.

* __History__: Discovered by Cagniard de la Tour in 1822.

* __Criticality__: The behaviour
of extended systems described as stochastic systems at a phase transition where scale invariance prevails.

* __Critical point__: The
set of values of the external parameters of a system at which its behavior
changes abruptly; Usually marks a phase transition, and the critical configuration
has characteristic scaling properties.

* __Approaches__: The traditional one uses dimensional analysis; Now one
often uses the renormalization group.

@ __Intros, reviews__: Bhattacharjee cm/00-ln;
Tobochnik AJP(01)mar
[and phase transitions, RL]; Brankov et al 02 [finite systems]; Christensen & Moloney 05 [and
complexity].

@ __History__:
Berche et al RBEF(09)-a0905 [Cagniard
de la Tour]; Baker JSP(10)
[last half century].

@ __Texts__: Ma 76; Stora & Osterwalder ed-86; Stanley 87; Binney 92;
Bak 96; Cardy 96; Zinn-Justin 96; Sornette 00; Amit & Martín-Mayor 05;
Herbut 07; Uzunov 10; Nishimori & Ortiz 11; Täuber 14.

**Self-Organized Criticality** > s.a. complexity.

* __Idea__: A situation in
which a complex system far from equilibrium organizes itself into a configuration
(statistically) describable by just a few parameters; It emerges from the
dynamics of extended, dissipative systems that evolve through a sequence of
metastable states into a critical state, with long range spatial and temporal
correlations; Central questions are, How does this happen? How do we extract
usable information from vast amounts
of data?

* __Modeling__: 2002, The
phenomenology is seen in many areas, but not well understood theoretically;
There are attempts at understanding and
modeling it using energy, statistics and information concepts; A tool that
may be useful is Paczuski's "metric" used to describe correlations between
events in earthquake studies.

* __Features__: A 1/*f* noise,
as opposed to white noise; Arises from the cooperative phenomena of many degrees
of freedom, giving rise to simple phenomena
in complex situations (in this sense, opposite to chaos).

@ __General references__: Bak et al PRL(87);
Kauffman 93 [in evolution];
Maslov & Zhang PhyA(96)ao [percolation,
transport model]; Jensen 98; Paczuski & Bak cm/99-proc;
Alava cm/03-ch
[as a phase transition]; Cessac
et al JSP(04)
[thermodynamic formalism]; Dhar PhyA(06)
[models]; Pruessner 12; Aschwanden ApJ(14)-a1310 [macroscopic description and astrophysical applications].

@ __Related topics__: Bak & Boettcher PhyD(97)cm [and
punctuated equilibrium];
Baiesi & Paczuski PRE(04)cm/03 [metric
for earthquakes]; Stapleton
et al JSP(04)
[sensitivity to initial conditions]; Yang JPA(04),
Marković & Gros PRP(14) [origin of power-law distributions].

**Examples and Phenomena** > s.a. geometric
phase; phase transitions; sigma
models; yang-mills gauge theory.

* __Applications__: The central
paradigm is the sand pile; Other common ones are earthquakes (the Earth's crust
may be in a self-organized critical state; & Maya
Paczuski), extinctions, economics, coast lines, language; Many can be classified
as "stick-slip" or "punctuated equilibrium" phenomena.

@ __Matter near criticality__: Bernevig et al AP(04)
[spectroscopy]; Gitterman 09 [chemical reactions]; > s.a. entanglement [scaling].

@ __Supercritical phenomena__: Maslov TMP(14) [two-fluid description].

@ __In general relativity__: Loustó PRD(95)gq/94 [black
holes, effective 2D description]; > s.a. critical
collapse; types of singularities.

@ __In quantum gravity__: Smolin LNP(95)gq [and
cosmology];
Ansari & Smolin CQG(08)-ht/04
[spin
network evolution and classical spacetime].

@ __Quantum critical phenomena__: Zanardi et al PRA(07)-a0707 [Bures metric
approach]; Kinross et al PRX(14) [in a model magnetic material]; > s.a. quantum correlations.

@ __Geometry, combinatorics__: Lise
& Paczuski PRL(02)cm,
Ráth & Tóth EJPr(09)-a0808 [random graph]; > s.a. dynamical
triangulations [surfaces], networks.

@ __Lattice and
spin systems__: Ruelle CMP(01)mp/00;
Ódor 08;
Eloranta a0909 [ice model, connectivity]; Argolo et al PhyA(11) [2D epidemic process].

@ __Other types of systems__: Creutz PhyA(04)
[sand piles]; Paczuski & Hughes PhyA(04)
[solar activity]; Turcotte & Malamud PhyA(04)
[examples]; Anisimov IJTh(11)-a1308 [in fluids]; Aschwanden et al SSR(16)-a1403 [solar physics and astrophysics, rev]; Chaté & Muñoz Phy(14) [insect swarms].

@ __Related topics__:
Ballhausen et al
PLB(04)ht/03 [continuous
dimension]; Barmatz et al RMP(07)
[in microgravity]; Jenkovszky et al IJMPA(10) [in deep inelastic scattering]; > s.a. Foam [polycrystals]; Percolation; Universality.

**Techniques and Related Topics**

@ __And renormalization group__:
Fisher RMP(74);
Wilson RMP(75), RMP(83);
Barber PRP(77);
Vicari PoS-a0709
[for multi-parameter *φ*^{4} theories];
Jona-Lasinio PTPS(10)-a1003-conf [conceptual]; Benedetti JSM(15)-a1403 [scalar fields, effects of curved background geometries].

@ __Field-theory techniques__: Bagnuls & Bervillier JPS(97)ht,
IJMPA(01)ht;
Zinn-Justin ht/98-proc;
Folk & Moser JPA(06)
[critical behavior in equilibrium]; Sokolov TMP(13) [critical behavior of 2D field theories and the renormalization group]; > s.a. Conformal
Field Theory.

@ __Related topics__: Robledo PhyA(04)
[and Tsallis statistics]; Davatolhagh AJP(06)may
[scaling laws, critical exponents].

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feb 2017