geometrical frustration - 2024 ARCADIA

Question

This property often occurs in systems with a pyrochlore lattice, which consists of tetrahedra connected by their vertices. For 10 points each:

[10h] Name this property of systems whose geometry prohibits them from simultaneously minimizing all interactions, resulting in many degenerate ground states. Exotic states like spin ice can occur in systems with this property.

ANSWER: geometrical frustration

[10e] Spin ice is named because the spins on a pyrochlore lattice are directly analogous to protons in water ice, so the two systems have the same residual value of this quantity. This quantity is equal to k times the log of the number of microstates.

ANSWER: entropy [or S]

[10m] Due to geometrical frustration, this property cannot occur in a triangular lattice. In this form of magnetism that occurs below the Néel (“nay-EL”) temperature, all neighboring spins point in [emphasize] opposite directions.

ANSWER: anti-ferromagnetism

<VD, Physics>

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Summary


2024 ARCADIA at BU	2024-12-06	Y	8	7.50	63%	13%	0%
2024 ARCADIA at Duke	2024-12-06	Y	3	13.33	67%	33%	33%
2024 ARCADIA at Missouri S&T	2024-12-06	Y	1	10.00	100%	0%	0%
2024 ARCADIA Online	2025-05-17	Y	5	20.00	100%	60%	40%
2024 ARCADIA at Penn State	2024-12-06	Y	2	5.00	50%	0%	0%
2024 ARCADIA at Florida Tech	2024-12-06	Y	4	15.00	75%	50%	25%
2024 ARCADIA at UC Berkeley	2024-12-06	Y	2	25.00	100%	50%	100%
2024 ARCADIA at Waterloo	2024-11-09	Y	6	13.33	67%	33%	33%
2024 ARCADIA at GT	2024-12-06	Y	3	16.67	100%	33%	33%
2024 ARCADIA at Illinois	2024-11-09	Y	4	22.50	100%	75%	50%
2024 ARCADIA at Warwick	2024-12-06	Y	5	12.00	100%	20%	0%
2024 ARCADIA at Claremont	2024-11-02	Y	3	16.67	100%	33%	33%

Data


Amherst	Boston University	0	10	0	10
Bowdoin C	Boston College A	0	0	0	0
Boston College B	Brandeis B	0	0	0	0
Bowdoin B	MIT	0	10	0	10
Tufts B	Clark House	0	10	0	10
Harvard	Clark Wilson	0	10	0	10
Tufts A	Bowdoin A	0	10	10	20
Brandeis A	Yale	0	0	0	0
South Carolina	Virginia Tech A	0	10	0	10
North Carolina A	Virginia Tech B	0	0	0	0
North Carolina B	Virginia Tech C	10	10	10	30
Missouri	WashU	0	10	0	10
In the Mood for Buzz	Madmen and Specialists	0	10	10	20
Social credit go vroom	Old and Young	0	10	0	10
Paddington in Peru (2024)	ASU->Stanford->ASU pipeline	10	10	0	20
Toyota Tundra Turbos — Twisting Truths - Tackling Trivia - Taming Titans	she limp on my waltz till i feel pathetique	0	10	10	20
bingy academy	The cult of SGA	10	10	10	30
Penn State	RIT	0	10	0	10
Maryland	Pitt	0	0	0	0
Florida Tech	UF C	0	10	0	10
UCF A	UCF B	0	10	10	20
UF B	Valencia	10	10	10	30
USF	UF A	0	0	0	0
Berkeley A	Berkeley Past	10	10	10	30
Stanford	Berkeley B	10	10	0	20
McGill A	Toronto Disband the Club 2k24	0	10	0	10
Waterloo Cloze	Waterloo Basic	0	10	0	10
Waterloo Aspidistra	Carleton A	10	10	10	30
Ottawa Absolomabsolomabsolom	Toronto B	0	0	0	0
Toronto A	Toronto Metropolitan A	10	10	10	30
Toronto Chestnut Rice and Kamehameha	McMaster ApocolocyntosisBidii	0	0	0	0
Georgia Tech D	Innovation Academy A	0	10	0	10
Johns Creek	Innovation Academy B	0	10	0	10
Georgia Tech A	Lambert	10	10	10	30
Notre Dame	Chicago B	0	10	0	10
Chicago A	Illinois Blue	10	10	10	30
Illinois Orange	Purdue B	10	10	10	30
Purdue A	SIUE	0	10	10	20
Imperial A	Warwick B	0	10	0	10
LSE B	Warwick C	0	10	0	10
Bristol	Cambridge A	0	10	0	10
Cambridge B	Southampton	0	10	10	20
Imperial B	Warwick A	0	10	0	10
SGV Ventures	Anderson et al.	0	10	10	20
Claremont	ALCU	0	10	0	10
U[C]SD	Jason et al.	10	10	0	20