# Ising spin vs Pauli spin matrices [closed]

Are Ising spins scalar or operators? I am not a condensed matter physicist hence having some confusion. I have learnt about Ising models from adiabatic quantum algorithm papers. For example this presentation or this paper encodes their quantum adiabatic algorithm for an Ising model. In an Ising model the spins are $\pm 1$. In his original adiabatic quantum computation paper, Farhi didn't mention about Ising models. Moreover he explicitly used Pauli's spin matrices and not the $\pm 1$ spins.

Can we use $\pm$ spins and Pauli's matrices interchangeability at least in the context of adiabatic quantum algorithms?

## closed as not constructive by KavehMay 31 '13 at 17:18

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance. If this question can be reworded to fit the rules in the help center, please edit the question.

• Copy on Physics. – Kaveh May 28 '13 at 17:50
• Please do not cross post simultaneously. It wastes effort on multiple locations. If you don't get a satisfactory answer on one site, you're welcome to repost on another one. – Suresh Venkat May 28 '13 at 23:10
• It appears that you have crossposted this question simultaneously. While we don't mind a question being reposted, our site policy prohibits simultaneous crossposting as it duplicates effort and fractures discussion. Crossposting is only permitted after sufficient time has passed and you have not obtained your desired answer elsewhere. When crossposting please summarize the relevant discussions from other sites in your question and link to the copies in both directions. – Kaveh May 31 '13 at 17:18
• @Kaveh, understood. – Omar Shehab May 31 '13 at 19:59

Neither, they are domain elements. Any two domain elements would do: $\{+1, -1\}$, $\{0,1\}$, $\{\text{cat}, \text{dog}\}$.
Physicists have wonderful imaginations and thus name certain parameters based on their physical intuition for the behavior of nature. In this case, they interpret the states of the particles interacting in the Ising model as either spinning up or down. Furthermore, opposite spins produce opposite effects, such as their resulting magnetic fields being the negative of each other. Thus, the state of the particles (i.e. the spins) are succinctly represented in the model as either $+1$ or $-1$.
The Potts model is a generalization of the Ising model. One of the generalizations is that each particle can take one of $q$ values (i.e. the domain size is now $q$). By continuing the intuitive naming from the Ising model, these $q$ states are also called spins.