Question
This second-order phase transition displays critical opalescence, as does the liquid–gas transition near its critical point. For 10 points each:
[10m] Name this phase transition that can be mapped to the liquid–gas phase transition by replacing the spins with particle occupation numbers. This phase transition occurs as temperature is lowered in the Ising model.
ANSWER: ferromagnetic phase transition [or paramagnetic-to-ferromagnetic phase transition; or answers indicating that the system is becoming ferromagnetic or a ferromagnet; prompt on magnetic phase transition or becoming magnetically ordered; prompt on answers that describe losing paramagnetism]
[10h] The Ising model and liquid–gas transition are in the same universality class, meaning that they have identical values for these quantities. Two of these quantities are related by the Josephson hyperscaling relation.
ANSWER: critical exponents [prompt on exponents]
[10e] Meanfield theory predicts correct critical exponents when this quantity is above its “upper critical” value. This quantity equals two for a square lattice and three for a cubic lattice.
ANSWER: dimension [or number of dimensions]
<Physics>
Summary
| 2024 ACF Regionals @ Berkeley | 01/27/2024 | Y | 3 | 23.33 | 100% | 100% | 33% |
| 2024 ACF Regionals @ Cornell | 01/27/2024 | Y | 3 | 13.33 | 100% | 33% | 0% |
| 2024 ACF Regionals @ JMU | 01/27/2024 | Y | 10 | 7.00 | 70% | 0% | 0% |
| 2024 ACF Regionals @ Nebraska | 01/27/2024 | Y | 6 | 6.67 | 67% | 0% | 0% |
| 2024 ACF Regionals @ Ohio State | 01/27/2024 | Y | 3 | 10.00 | 67% | 33% | 0% |
| 2024 ACF Regionals @ Rutgers | 01/27/2024 | Y | 5 | 10.00 | 60% | 20% | 20% |
| 2024 ACF Regionals @ Imperial | 01/27/2024 | Y | 8 | 10.00 | 88% | 13% | 0% |
| 2024 ACF Regionals @ Vanderbilt | 01/27/2024 | Y | 5 | 8.00 | 60% | 20% | 0% |
| 2024 ACF Regionals @ MIT | 01/27/2024 | Y | 4 | 17.50 | 100% | 50% | 25% |
Data
| Stanford A | Berkeley A | 10 | 0 | 10 | 20 |
| Berkeley B | Berkeley C | 10 | 0 | 10 | 20 |
| Stanford B | Stanford C | 10 | 10 | 10 | 30 |