Question
Lars Onsager used a transfer-matrix method to analytically solve a model describing this phenomenon in 2D. For 10 points each:
[10m] Name this phenomenon that is modeled by a lattice of interacting spins in the Ising model. In nature, this phenomenon typically has no net effect because it only occurs within microscopic “domains.”
ANSWER: ferromagnetism [accept word forms; prompt on word forms of magnetism]
[10e] The 2D Ising model is one of the simplest models that can exhibit these processes exemplified by sublimation and deposition.
ANSWER: phase transitions [or phase changes]
[10h] The Ising model is often studied with these numerical simulation methods, exemplified by the Metropolis–Hastings algorithm, that traverse a system’s state space with stochastic steps that depend only on the current state.
ANSWER: Markov chain Monte Carlo methods [or MCMC methods; prompt on Monte Carlo methods or MC methods]
<Benjamin Chapman, Science - Physics> ~20909~ <Editor: David Bass>
Summary
| 2023 PACE NSC | 06/10/2023 | Y | 35 | 14.86 | 94% | 54% | 0% |
Data
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| Irvington A | Parkway West | 10 | 10 | 0 | 20 |
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| Mercer County | Detroit Catholic Central B | 0 | 10 | 0 | 10 |
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