Editing Spin glass (section)

==History==

A detailed account of the history of spin glasses from the early 1960s to the late 1980s can be found in a series of popular articles by [[Philip Warren Anderson|Philip W. Anderson]] in ''[[Physics Today]]''.<ref>
{{cite journal
 |title=Spin Glass I: A Scaling Law Rescued
 |journal = Physics Today|volume = 41|pages = 9–11|author=Philip W. Anderson
 |year=1988
 |issue = 1|doi=10.1063/1.2811268
 |url=http://www.physics.rutgers.edu/~pchandra/physics681/sglass1.pdf
 |bibcode=1988PhT....41a...9A
 }}</ref><ref>
{{cite journal
 |title=Spin Glass II: Is There a Phase Transition?
 |journal = Physics Today|volume = 41|issue = 3|pages = 9|author=Philip W. Anderson
 |year=1988
 |doi=10.1063/1.2811336
 |url=http://www.physics.rutgers.edu/~pchandra/physics681/sglass2.pdf |bibcode=1988PhT....41c...9A
 }}</ref><ref>
{{cite journal
 |title=Spin Glass III: Theory Raises its Head
 |journal = Physics Today|volume = 41|issue = 6|pages = 9–11|author=Philip W. Anderson
 |year=1988
 |doi=10.1063/1.2811440
 |url=http://www.physics.rutgers.edu/~pchandra/physics681/sglass3.pdf |bibcode=1988PhT....41f...9A
 }}</ref><ref>
{{cite journal
 |title=Spin Glass IV: Glimmerings of Trouble
 |journal = Physics Today|volume = 41|issue = 9|pages = 9–11|author=Philip W. Anderson
 |year=1988
 |doi=10.1063/1.881135
 |url=http://www.physics.rutgers.edu/~pchandra/physics681/sglass4.pdf |bibcode=1988PhT....41i...9A
 }}</ref><ref>
{{cite journal
 |title=Spin Glass V: Real Power Brought to Bear
 |journal = Physics Today|volume = 42|issue = 7|pages = 9–11|author=Philip W. Anderson
 |year=1989
 |doi=10.1063/1.2811073
 |url=http://www.physics.rutgers.edu/~pchandra/physics681/sglass5.pdf |bibcode=1989PhT....42g...9A
 }}</ref><ref>
{{cite journal
 |title=Spin Glass VI: Spin Glass As Cornucopia
 |journal = Physics Today|volume = 42|issue = 9|pages = 9–11|author=Philip W. Anderson
 |year=1989
 |doi=10.1063/1.2811137
 |url=http://www.physics.rutgers.edu/~pchandra/physics681/sglass6.pdf |bibcode=1989PhT....42i...9A
 }}</ref><ref>
{{cite journal
 |title=Spin Glass VII: Spin Glass as Paradigm
 |journal = Physics Today|volume = 43|issue = 3|pages = 9–11|author=Philip W. Anderson
 |year=1990
 |doi=10.1063/1.2810479
 |url=http://www.physics.rutgers.edu/~pchandra/physics681/sglass7.pdf |bibcode=1990PhT....43c...9A
 }}</ref><ref>[https://web.archive.org/web/20240206131352/https://pitp.phas.ubc.ca/confs/7pines2009/readings/Stamp-PWA-SpinGl-refF-PhysT.pdf All of them combined.]</ref>

=== Discovery ===
In 1930s, material scientists discovered the [[Kondo effect]], where the resistivity of nominally pure gold reaches a minimum at 10 K, and similarly for nominally pure Cu at 2 K. It was later understood that the Kondo effect occurs when a nonmagnetic metal contains a very small fraction of magnetic atoms (i.e., at high dilution).

Unusual behavior was observed in iron-in-gold alloy (Au''Fe'') and manganese-in-copper alloy (Cu''Mn'') at around 1 to 10 [[Atomic ratio|atom percent]]. Cannella and Mydosh observed in 1972<ref>{{Cite journal |last1=Cannella |first1=V. |last2=Mydosh |first2=J. A. |date=1972-12-01 |title=Magnetic Ordering in Gold-Iron Alloys |url=https://link.aps.org/doi/10.1103/PhysRevB.6.4220 |journal=Physical Review B |volume=6 |issue=11 |pages=4220–4237 |doi=10.1103/PhysRevB.6.4220|bibcode=1972PhRvB...6.4220C }}</ref> that Au''Fe'' had an unexpected cusplike peak in the [[Magnetic susceptibility|a.c. susceptibility]] at a well defined temperature, which would later be termed ''spin glass freezing temperature''.<ref>{{Cite journal |last1=Mulder |first1=C. A. M. |last2=van Duyneveldt |first2=A. J. |last3=Mydosh |first3=J. A. |date=1981-02-01 |title=Susceptibility of the $\mathrm{Cu}\mathrm{Mn}$ spin-glass: Frequency and field dependences |url=https://link.aps.org/doi/10.1103/PhysRevB.23.1384 |journal=Physical Review B |volume=23 |issue=3 |pages=1384–1396 |doi=10.1103/PhysRevB.23.1384}}</ref>

It was also called "mictomagnet" (micto- is Greek for "mixed"). The term arose from the observation that these materials often contain a mix of ferromagnetic (<math>J > 0</math>) and antiferromagnetic (<math>J < 0</math>) interactions, leading to their disordered magnetic structure. This term fell out of favor as the theoretical understanding of spin glasses evolved, recognizing that the magnetic frustration arises not just from a simple mixture of ferro- and antiferromagnetic interactions, but from their randomness and frustration in the system.

=== Sherrington–Kirkpatrick model ===

Sherrington and Kirkpatrick proposed the SK model in 1975, and solved it by the replica method.<ref>{{Cite journal |last1=Sherrington |first1=David |last2=Kirkpatrick |first2=Scott |date=1975-12-29 |title=Solvable Model of a Spin-Glass |url=http://dx.doi.org/10.1103/physrevlett.35.1792 |journal=Physical Review Letters |volume=35 |issue=26 |pages=1792–1796 |doi=10.1103/physrevlett.35.1792 |bibcode=1975PhRvL..35.1792S |issn=0031-9007}}</ref> They discovered that at low temperatures, its entropy becomes negative, which they thought was because the replica method is a heuristic method that does not apply at low temperatures.

It was then discovered that the replica method was correct, but the problem lies in that the low-temperature broken symmetry in the SK model cannot be purely characterized by the Edwards-Anderson order parameter. Instead, further order parameters are necessary, which leads to replica breaking ansatz of [[Giorgio Parisi]]. At the full replica breaking ansatz, infinitely many order parameters are required to characterize a stable solution.<ref>{{Cite journal |last=Parisi |first=G. |date=1979-12-03 |title=Infinite Number of Order Parameters for Spin-Glasses |url=https://link.aps.org/doi/10.1103/PhysRevLett.43.1754 |journal=Physical Review Letters |language=en |volume=43 |issue=23 |pages=1754–1756 |doi=10.1103/PhysRevLett.43.1754 |bibcode=1979PhRvL..43.1754P |issn=0031-9007}}</ref>