exchange interaction - 2025 ACF Fall

Question

This interaction causes triplet spin states to have lower energy than singlet states. For 10 points each:

[10h] Name this interaction caused by the indistinguishability of quantum particles. By the spin-statistics theorem, fermion wavefunctions are antisymmetric under this interaction while boson wavefunctions are symmetric.

ANSWER: exchange interaction

[10m] The exchange interaction couples neighboring spins in the Ising model, which explains this phenomenon. This phenomenon occurs when domains in a solid spontaneously align.

ANSWER: ferromagnetism [prompt on magnetism]

[10e] This scientist names the Hamiltonian describing spins in a lattice and discovered the exchange interaction independently of Paul Dirac. This scientist discovered the uncertainty principle.

ANSWER: Werner Heisenberg [accept Heisenberg Hamiltonian; accept Heisenberg uncertainty principle]

<Editors, Physics>

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Summary


Northern California	Main	Y	4	20.00	100%	50%	50%
Southern California	Main	Y	7	12.86	100%	14%	14%
Eastern Canada (1)	Main	Y	5	14.00	100%	40%	0%
Eastern Canada (2)	Main	Y	9	14.44	100%	44%	0%
Florida	Main	Y	4	12.50	100%	25%	0%
Great Lakes	Main	Y	11	15.45	91%	64%	0%
Lower Mid-Atlantic	Main	Y	9	14.44	89%	56%	0%
Upper Mid-Atlantic	Main	Y	12	15.00	100%	50%	0%
Midwest	Main	Y	9	13.33	100%	33%	0%
North	Main	Y	4	10.00	100%	0%	0%
Northeast	Main	Y	12	10.83	92%	17%	0%
Pacific	Main	Y	8	12.50	88%	38%	0%
South Central	Main	Y	7	10.00	86%	14%	0%
Southeast	Main	Y	13	12.31	92%	31%	0%
UK (North)	UK	Y	5	14.00	100%	40%	0%
UK (South)	UK	Y	8	12.50	100%	25%	0%
Upstate NY	Main	Y	5	10.00	100%	0%	0%

Data


Berkeley Boss Bandit	Berkeley Archer Queen	0	0	10	10
Stanford B	Berkeley Mighty Miner	10	10	10	30
Berkeley Skeleton King	Stanford A	10	0	10	20
Berkeley Little Prince	UCSC	0	10	10	20
UCLA B	Claremont A	10	10	10	30
UCLA E	UC Irvine	0	0	10	10
UCSD A	UCLA A	0	0	10	10
UCLA F	UC Santa Barbara	0	0	10	10
UCSD B	UCLA D	0	0	10	10
Claremont B	USC A	0	0	10	10
Claremont C	USC B	0	0	10	10
McGill A	Ottawa A	0	0	10	10
McGill B	McGill C	0	10	10	20
Carleton B	McGill E	0	0	10	10
Ottawa B	Ottawa D	0	0	10	10
Carleton A	Ottawa C	0	10	10	20
McMaster C	Queen's A	0	0	10	10
Toronto I	Brock A	0	0	10	10
McMaster B	Guelph A	0	10	10	20
Toronto D	Toronto B	0	0	10	10
Toronto G	Waterloo C	0	0	10	10
Toronto F	Toronto H	0	10	10	20
Waterloo A	Toronto C	0	10	10	20
Toronto E	Waterloo B	0	0	10	10
Toronto A	McMaster A	0	10	10	20
South Florida A	ERAU Daytona A	0	0	10	10
Florida A	Florida Tech A	0	0	10	10
UCF A	Florida B	0	10	10	20
Florida State A	Florida Tech B	0	0	10	10
CWRU A	Michigan D	0	10	10	20
CWRU B	CWRU C	0	10	10	20
CWRU D	Michigan State A	0	0	10	10
Kentucky	Michigan State D	0	10	0	10
Louisville D	Ohio State D	0	10	10	20
Michigan C	Louisville C	0	0	10	10
Michigan A	Michigan State C	0	10	10	20
Ohio State B	Pittsburgh	0	0	10	10
Ohio State A	WVU B	0	10	10	20
Michigan State B	Ohio State C	0	0	10	10
Louisville B	Louisville A	0	10	10	20
Duke A	William & Mary B	0	0	10	10
NCSU A	Virginia Tech B	0	10	10	20
NCSU B	Tusculum A	0	0	10	10
UNC D	UNC C	0	10	10	20
Virginia Tech C	VCU A	0	10	10	20
Virginia A	Virginia Tech A	0	10	10	20
JMU A	William & Mary C	0	0	10	10
William & Mary A	UNC A	0	10	10	20
JMU B	Liberty C	0	0	0	0
Johns Hopkins	Columbia A	0	10	10	20
Stony Brook	George Mason C	0	10	10	20
Maryland C	Lehigh A	0	0	10	10
NYU A	George Mason B	0	10	10	20
Penn	Vassar B	0	10	10	20
Maryland A	Princeton	0	0	10	10
Columbia B	Rowan	0	0	10	10
Vassar A	Rutgers A	0	0	10	10
Maryland B	Rutgers B	0	10	10	20
NYU B	Rutgers C	0	0	10	10
George Mason A	Rutgers D	0	10	10	20
Lehigh B	NYU C	0	0	10	10
WashU Grizzlers	Chicago B	0	0	10	10
Illinois Blue	Illinois Canada	0	10	10	20
Illinois Champaign	William Woods University A	0	0	10	10
Purdue B	Indiana A	0	10	10	20
Chicago A	Indiana B	0	10	10	20
Purdue D	Iowa B	0	0	10	10
WashU Grolars	Rose-Hulman A	0	0	10	10
Illinois Orange	Purdue C	0	0	10	10
Illinois Urbana	Iowa A	0	0	10	10
Minnesota	Michigan Tech	0	0	10	10
Iowa State	St. Thomas	0	0	10	10
Macalester	Wisconsin A	0	0	10	10
Wisconsin C	Wisconsin B	0	0	10	10
Boston College B	Vermont A	0	0	10	10
Boston University B	Brandeis Beethoven	0	10	10	20
Vermont B	Brandeis Mozart	0	0	10	10
Brown A	Tufts C	0	0	10	10
Dartmouth A	Amherst B	0	0	10	10
Dartmouth B	Boston University A	0	0	10	10
Dartmouth C	MIT B	0	0	0	0
Tufts A	UConn A	0	0	10	10
Williams A	Southern Connecticut State University A	0	10	10	20
Williams C	Brandeis Bach	0	0	10	10
Williams B	Amherst A	0	0	10	10
Tufts B	Boston College A	0	0	10	10
British Columbia C	Arizona State A	0	0	10	10
Washington Sockeye	Boise State	0	0	10	10
British Columbia A	Washington Atlantic	0	0	10	10
Alberta A	British Columbia B	0	0	10	10
Washington Masu	Alberta B	0	0	0	0
Washington Pink	Washington State	0	10	10	20
Arizona State B	Texas	0	10	10	20
Washington Chinook	Washington Coho	0	10	10	20
Rose State	Central Oklahoma B	0	0	10	10
Harding	Kansas State A	0	0	10	10
Kansas State B	Tulsa B	0	0	0	0
Nebraska A	Murray State College B	0	0	10	10
Nebraska B	Murray State College A	0	0	10	10
Nebraska C	Tulsa A	0	0	10	10
Central Oklahoma A	Oklahoma	0	10	10	20
Alabama A	Clemson A	0	10	10	20
Tennessee Tech	Auburn B	0	0	10	10
Auburn C	Vanderbilt B	0	0	10	10
Clemson B	Tennessee B	0	0	10	10
South Carolina A	Georgia Tech A	0	10	10	20
Auburn A	Georgia Tech B	0	0	10	10
Sewanne	Georgia Tech D	0	0	0	0
Georgia Tech C	Tennessee A	0	0	10	10
Emory A	Georgia Tech F	0	10	10	20
Georgia A	Georgia Tech E	0	0	10	10
Chipola College	Vanderbilt A	0	10	10	20
Mississippi State A	Vanderbilt C	0	0	10	10
Sheffield B	Edinburgh C	0	0	10	10
York	Edinburgh B	0	0	10	10
Cardiff	Bristol	0	0	10	10
Cambridge A	Southampton	0	0	10	10
Birmingham	Cambridge C	0	0	10	10
Oxford	Cambridge E	0	0	10	10
Imperial A	Cambridge D	0	0	10	10
Cambridge B	Imperial C	0	10	10	20
Imperial D	Imperial B	0	10	10	20
LSE	Warwick	0	0	10	10
Durham A	Durham B	0	10	10	20
Edinburgh A	Durham C	0	10	10	20
Montevallo	Clemson C	0	0	10	10
Binghamton A	Cornell D	0	0	10	10
Sheffield A	Durham D	0	0	10	10
RIT A	Rochester	0	0	10	10
Cornell A	Cornell C	0	0	10	10
RIT B	ESF	0	0	10	10
Cornell B	Binghamton B	0	0	10	10