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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