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; Self-Organization.
* 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 φ⁴ 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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