Coupled-Spin Models  

In General > s.a. path integrals; quantum spin models; spinors in field theory; statistical mechanics.
* Frustration: A situation in the classical theory in which there is little or no long-range ordering between coupled lattice sites in the ground state, e.g., in spin-glass theory with a tetrahedral lattice, there are antiferromagnetic couplings between magnetic spins that cannot be antiparallel.
@ General references: De las Cuevas et al PRL(09)-a0901, NJP(10) [all classical spin models, and lattice gauge theory]; Dutta et al a1012-RMP [rev]; Jonckheere et al IEEE(12)-a1202 [geometric approach]; Duivenvoorden & Quella PRB(13)-a1206 [topological phases]; focus Phy(12) [model for spin ice]; Naaijkens a1311-ln [infinite lattices, mathematical]; Bodneva & Lundin TMP(14) [reduction to diffusion equation and dynamical chaos]; De las Cuevas & Cubitt Sci(16)mar-a1406 ["fine-graining" and universal models]; Garon et al PRA(15)-a1409 [visualizing operators].
@ Frustration: Lee et al Nat(02)aug [emergent excitations]; Moessner & Ramírez PT(06)feb; Koma a0805 [topology]; Richert PLA(08) [Berry phase as test for low-energy spectrum]; Normand CP(09); Diep 13.
@ Large-scale, effective quantum field theory: Bény a1511; > s.a. field theory.
@ Thermodynamics: Rojas et al JMP(02) [high-T expansion]; Berche & López EJP(06) [pedagogic]; Benedetti & Loll PhyA(07) [coupled to causal dynamically triangulated lattice]; Wilms et al JSM(11)-a1011 [classical many-body correlations and mutual information]; > s.a. entropy; temperature.
@ Related topics: Latora et al PRE(01)cm, PhyA(02)cm/01 [and thermodynamic limit]; Wesenberg & Mølmer PRA(02)qp [mixed states]; Albertini & D'Alessandro qp/03 [determining H experimentally]; Babadi et al PRX(15) [relaxation dynamics]; Kastoryano & Lucia a1705 [lower bounds on the spectral gap].

Spin Glasses > s.a. chaotic systems; Spin Liquid.
@ General references: Binder & Young RMP(86); Mézard et al 86; Dotsenko 95; Ciliberti & Marinari JSP(04)cm/03 [ultrametricity]; Dias Barreto & Fidaleo CMP(04) [KMS states]; Janutka PS(05) [sound propagation]; De Dominicis & Giardina 06 [and random fields]; Parisi JPA(08) [finite-dimensional]; Contucci & Giardinà 12; Stein & Newman 13 [and complexity; r PT(14)jan]; Arguin et al JSP(14)-a1403 [interface free energies].
@ Critical phenomena: Nishimori & Ohzeki PhyA(10) [multicritical point]; Koh & Kwek PLA(14) [renormalization-group approach].
@ Mean-field theory: Chowdhury & Mookerjee PRP(84); Guerra & Toninelli JPA(03); Guerra in(05)cm/04; Koukiou a0806 [lower bound on ground state energy]; Parisi LMP(09) [heuristic replica approach]; Talagrand 11.

Other Models > s.a. lattice gauge theories [duality]; spin networks in quantum gravity.
* Spin chains: One-dimensional arrangements of many spins.
@ Two spins: Emerson & Ballentine PRA(01)qp/00, PRE(01)qp [quantum/classical]; Lednicky & Lyuboshitz PLB(01) [correlations]; D'Alessandro qp/03 [electromagnetic field, measurements]; Zobov a1211-conf [correlations, high-temperature dynamics]; Zobov QCC-a1211-conf [quantum dynamics].
@ Spin chains: Ribeiro & Klümper NPB(08), Sarkar NPB(08) [antiferromagnetic]; Joel et al AJP(13)jun-a1209 [introduction to spectrum, symmetries, and dynamics]; Genovese Phy(15)-a1408 [with impurities]; Vernier et al a1601 [continuum limit]; Benatti et al a1606 [dissipatively generated quantum correlations].
@ Other many-spin models: Godrèche & Luck JPA(00) [ferromagnetic, quenched]; Carbone et al NPB(01)gq/00 [hierarchies]; Albertini & D'Alessandro qp/01 [Lie-algebra structure]; Shik et al NPB(03) [soluble]; van Enter & Ruszel JSP(07)mp/06 [chaotic T = 0 limit]; Verbeure JPA(09) [long-range order]; Morais & Procacci a0907 [integer-spin systems without phase transitions]; Ragni et al LNCS(13)-a1405 [spin networks, Racah coefficients]; Arad et al JSM(16)-a1406 [relationship between measurement outcomes of local and global Hamiltonians]; Schachenmayer et al PRX(15)-a1408 [truncated Wigner approximation]; Santos et al PRL(16)-a1507 [with long-range interactions, cooperative Zeno shielding]; > s.a. statistical-mechanical systems.
@ One spin + other system: Ballentine PRA(91), PRA(91) [+ polarized beam of spins]; Semin et al PRA(14), Bhattacharya et al a1610 [and spin bath].
@ Model for light propagation: Wen PRB(03); Hamma et al PRL(09)-a0808 [speed].
@ Integrable: Prosen JPA(98); Steinigeweg & Schmidt MPAG(09)mp/05; > s.a. integrable systems.
@ Heisenberg models: Schmidt JPA(02)cm [energy bounds]; Subrahmanyam PRA(04)qp/03, PRA(04)qp/03 [entanglement]; Santos et al PRA(04)qp/03 [chaos and entanglement]; Wang et al JPA(05)qp [spin-1, entanglement]; Nachtergaele & Starr in(06)mp/05 [energy levels]; Kumar et al PLA(06) [2+1 continuum, non-integrability]; Kapikranian et al JPA(07) [2D, ordering]; Brown et al PRE(08)-a0707 [chaos and entanglement]; Bernatska & Holod TMP(09) [topological excitations]; Goldschmidt et al a1104-in [quantum, cycle and loop representations]; Moreno-Cardoner et al PRB(14)-a1402 [triangular lattice, Cluster Mean-Field approach]; Lees JMP(14)-a1406 [long-range order]; Schmidt a1701 [theory of ground states]; > s.a. Bethe Ansatz; entanglement entropy.
@ XXZ Heisenberg model: Razumov & Stroganov JPA(01), JPA(01)cm; Fessatidis et al PLA(08) [ground state, t-expansion method]; Nienhuis et al JSM(09)-a0808 [entanglement and finite-size effects]; Trippe et al JSM(12)-a0912 [triple point]; > s.a. entanglement entropy.
@ Other lattices: Nepomechie IJMPB(99)ht/98-proc [XXX model, introduction]; Anglès d'Auriac et al JPA(01) [hyperbolic lattice]; Wootters JMP(02)qp [parallel transport]; Ercolessi MPLA(03) [history]; Christandl et al PRL(04)qp/03 [qubit networks]; Yarotsky JMP(04) [perturbations, ground state].
@ Random lattices: Janke PhyA(00) [2D Potts]; Janke & Johnston NPB(00)hl/99 [Ising and Potts]; Grimmett 06 [random-cluster method]; Bovier & Kurkova JSP(07) [energy statistics]; Burrell & Osborne PRL(07)qp [disordered XY model, information propagation].

Other Models > see Bloch Equations; dirac fields; ising models; lattice field theory; SU(2); supersymmetric field theories; XY Chain.


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