Coupled-Spin Models| 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 LNP(17)-a1311 [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 NJP(17)-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 JSM(18)-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];
Auffinger & Jagannath JSP(19)-a1802 [generic p-spin models, spin distributions].
@ 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; types of entropies [Rényi entropy].
* 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 TMP(13)-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 NPB(16)-a1601 [continuum limit];
Benatti et al JMP(16)-a1606 [dissipatively generated quantum correlations];
> s.a. entangled, ergodic
systems; geometric phase; quantum spin models;
renormalization; statistical mechanics;
supersymmetric.
@ 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 JSP(09)-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 PRA(17)-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: 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];
> s.a. XXX Model.
@ 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].
> Related topics:
see Bloch Equations; ising models;
SU(2); supersymmetric field theories;
XY Chain.
> And other fields: see dirac fields;
Jordan-Wigner Transformations; lattice field theory.
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