Editing Potts model (section)

=== Generalized Potts model ===
A generalization of the Potts model is often used in statistical inference and biophysics, particularly for modelling proteins through [[direct coupling analysis]].<ref name=":1">{{Cite journal |last1=Shimagaki |first1=Kai |last2=Weigt |first2=Martin |date=2019-09-19 |title=Selection of sequence motifs and generative Hopfield-Potts models for protein families |url=https://link.aps.org/doi/10.1103/PhysRevE.100.032128 |journal=Physical Review E |volume=100 |issue=3 |pages=032128 |arxiv=1905.11848 |bibcode=2019PhRvE.100c2128S |doi=10.1103/PhysRevE.100.032128 |pmid=31639992 |s2cid=167217593}}</ref><ref>{{Cite journal |last1=Mehta |first1=Pankaj |last2=Bukov |first2=Marin |last3=Wang |first3=Ching-Hao |last4=Day |first4=Alexandre G. R. |last5=Richardson |first5=Clint |last6=Fisher |first6=Charles K. |last7=Schwab |first7=David J. |date=2019-05-30 |title=A high-bias, low-variance introduction to Machine Learning for physicists |journal=Physics Reports |volume=810 |pages=1–124 |arxiv=1803.08823 |bibcode=2019PhR...810....1M |doi=10.1016/j.physrep.2019.03.001 |issn=0370-1573 |pmc=6688775 |pmid=31404441}}</ref> This generalized Potts model consists of 'spins' that each may take on <math>q</math> states: <math>s_i \in \{1,\dots,q\}</math> (with no particular ordering). The Hamiltonian is,
: <math>
H = \sum_{i < j} J_{ij}(s_i,s_j) + \sum_i h_i(s_i),
</math>
where <math>J_{ij}(k,k')</math> is the energetic cost of spin <math>i</math> being in state <math>k</math> while spin <math>j</math> is in state <math>k'</math>, and <math>h_i(k)</math> is the energetic cost of spin <math>i</math> being in state <math>k</math>. Note: <math>J_{ij}(k,k') = J_{ji}(k',k)</math>. This model resembles the [[Sherrington-Kirkpatrick model]] in that couplings can be heterogeneous and non-local. There is no explicit lattice structure in this model.