Question
If heated above a critical “freezing temperature,” these systems transition to an ordered structure. For 10 points each:
[10m] Name these systems which exhibit geometrical frustration and are described by the Edwards-Anderson model. They consist of a lattice of magnetic dipoles with random alignment.
ANSWER: spin glasses
[10e] One can characterize the phase transition to a spin glass by computing the average of this quantity, which equals negative kT times the average of the log of the partition function. This quantity named for a German scientist is defined as “U minus TS.”
ANSWER: Helmholtz free energy [reject “Gibbs free energy” or “energy”]
[10h] Computing the average of the logarithm of the partition function is hard, but, amazingly, it's somehow easier to use this technique, where you make n identical copies of the system, instead compute the average of the partition function raised to the n power, minus 1, all over n, then take the limit as n approaches zero.
ANSWER: replica trick [or replica method]
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Summary
| 2023 BHSU @ Berkeley | 03/18/2023 | Y | 3 | 16.67 | 100% | 67% | 0% |
| 2023 BHSU @ Maryland | 03/11/2023 | Y | 3 | 13.33 | 100% | 33% | 0% |
| 2023 BHSU @ Northwestern | 02/25/2023 | Y | 6 | 15.00 | 83% | 50% | 17% |
| 2023 BHSU Online | 04/15/2023 | Y | 4 | 22.50 | 100% | 75% | 50% |
| 2023 BHSU @ Sheffield | 04/15/2023 | Y | 2 | 5.00 | 50% | 0% | 0% |
| 2023 BHSU @ Waterloo | 04/15/2023 | Y | 3 | 13.33 | 67% | 33% | 33% |
| 2023 BHSU @ Yale | 04/08/2023 | Y | 3 | 13.33 | 0% | 33% | 100% |
| 2023 BHSU @ Yale | 04/08/2023 | Y | 3 | 13.33 | 100% | 33% | 0% |
Data
| Broken Imperial Nomads | Oxford Hornets | 0 | 10 | 0 | 10 |
| Buzzers Karamazov | Magisters Ludi | 0 | 0 | 0 | 0 |