385:
225:
256:. The basic idea of the HS transformation is to reformulate a system of particles interacting through two-body potentials into a system of independent particles interacting with a fluctuating field. The procedure is widely used in
69:
276:. A major difficulty arising in the simulation with such field theories is their highly oscillatory nature in case of strong interactions, which leads to the well-known
254:
280:. The problem originates from the repulsive part of the interaction potential, which implicates the introduction of the complex factor via the HS transformation.
220:{\displaystyle \exp \left\{-{\frac {a}{2}}x^{2}\right\}={\sqrt {\frac {1}{2\pi a}}}\;\int _{-\infty }^{\infty }\exp \left\,dy,}
426:
400:
455:
445:
272:
The resulting field theories are well-suited for the application of effective approximation techniques, like the
32:
392:
273:
40:
344:
419:
315:
277:
56:
36:
233:
353:
324:
8:
450:
48:
357:
328:
313:
Stratonovich, R.L. (1958). "On a Method of
Calculating Quantum Distribution Functions".
412:
361:
44:
257:
60:
396:
52:
439:
365:
384:
29:
261:
342:
Hubbard, J. (1959). "Calculation of
Partition Functions".
299:Об одном методе вычисления квантовых функций распределения
267:
236:
72:
248:
219:
437:
420:
312:
296:
427:
413:
135:
63:. It is defined via the integral identity
207:
55:in the many-body interaction term of the
341:
268:Calculation of resulting field theories
438:
39:and popularized by British physicist
379:
264:, and electronic structure theory.
13:
149:
144:
14:
467:
383:
335:
290:
260:, classical particle physics,
35:invented by Russian physicist
1:
283:
399:. You can help Knowledge by
297:Стратонович, Р. Л. (1957).
7:
10:
472:
378:
43:. It is used to convert a
393:condensed matter physics
366:10.1103/PhysRevLett.3.77
298:
274:mean field approximation
230:where the real constant
345:Physical Review Letters
311:Translation available:
456:Condensed matter stubs
446:Functions and mappings
395:-related article is a
316:Soviet Physics Doklady
278:numerical sign problem
250:
249:{\displaystyle a>0}
221:
61:auxiliary scalar field
37:Ruslan L. Stratonovich
251:
222:
234:
70:
47:into its respective
18:Hubbard–Stratonovich
358:1959PhRvL...3...77H
329:1957SPhD....2..416S
153:
59:and introducing an
51:by linearizing the
246:
217:
136:
408:
407:
262:spin glass theory
188:
133:
132:
95:
463:
429:
422:
415:
387:
380:
370:
369:
339:
333:
332:
310:
294:
255:
253:
252:
247:
226:
224:
223:
218:
206:
202:
189:
187:
179:
178:
169:
152:
147:
134:
131:
117:
116:
111:
107:
106:
105:
96:
88:
53:density operator
471:
470:
466:
465:
464:
462:
461:
460:
436:
435:
434:
433:
376:
374:
373:
340:
336:
309:(6): 1097–1100.
303:Доклады АН СССР
300:
295:
291:
286:
270:
258:polymer physics
235:
232:
231:
180:
174:
170:
168:
164:
160:
148:
140:
121:
115:
101:
97:
87:
83:
79:
71:
68:
67:
45:particle theory
12:
11:
5:
469:
459:
458:
453:
448:
432:
431:
424:
417:
409:
406:
405:
388:
372:
371:
334:
305:(in Russian).
288:
287:
285:
282:
269:
266:
245:
242:
239:
228:
227:
216:
213:
210:
205:
201:
198:
195:
192:
186:
183:
177:
173:
167:
163:
159:
156:
151:
146:
143:
139:
130:
127:
124:
120:
114:
110:
104:
100:
94:
91:
86:
82:
78:
75:
33:transformation
26:transformation
9:
6:
4:
3:
2:
468:
457:
454:
452:
449:
447:
444:
443:
441:
430:
425:
423:
418:
416:
411:
410:
404:
402:
398:
394:
389:
386:
382:
381:
377:
367:
363:
359:
355:
351:
347:
346:
338:
330:
326:
322:
318:
317:
308:
304:
293:
289:
281:
279:
275:
265:
263:
259:
243:
240:
237:
214:
211:
208:
203:
199:
196:
193:
190:
184:
181:
175:
171:
165:
161:
157:
154:
141:
137:
128:
125:
122:
118:
112:
108:
102:
98:
92:
89:
84:
80:
76:
73:
66:
65:
64:
62:
58:
54:
50:
46:
42:
38:
34:
31:
27:
23:
19:
401:expanding it
390:
375:
349:
343:
337:
320:
314:
306:
302:
292:
271:
229:
49:field theory
41:John Hubbard
30:mathematical
28:is an exact
25:
21:
17:
15:
57:Hamiltonian
451:Transforms
440:Categories
284:References
352:(2): 77.
191:−
166:−
158:
150:∞
145:∞
142:−
138:∫
126:π
85:−
77:
354:Bibcode
325:Bibcode
323:: 416.
391:This
397:stub
241:>
16:The
362:doi
307:115
155:exp
74:exp
442::
360:.
348:.
319:.
301:.
24:)
22:HS
428:e
421:t
414:v
403:.
368:.
364::
356::
350:3
331:.
327::
321:2
244:0
238:a
215:,
212:y
209:d
204:]
200:y
197:x
194:i
185:a
182:2
176:2
172:y
162:[
129:a
123:2
119:1
113:=
109:}
103:2
99:x
93:2
90:a
81:{
20:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
