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Volumn 79, Issue 5, 2009, Pages

Mean-value identities as an opportunity for Monte Carlo error reduction

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL VARIATES; CPU TIME; DYSON EQUATIONS; ERROR REDUCTION; FIELD THEORY; GAIN FACTORS; MEAN VALUES; MONTE CARLO; MONTE CARLO SIMULATION; NUMBER GENERATOR; PSEUDO RANDOM; STATISTICAL ERRORS; THERMALIZATION; TWO-DIMENSIONAL ISING MODEL;

EID: 66749174537     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.051109     Document Type: Article
Times cited : (17)

References (32)
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    • For disordered systems, the time average in Eq. 9 is followed by a disorder average, which strongly diminishes the influence of the particular Monte Carlo dynamics.
    • For disordered systems, the time average in Eq. 9 is followed by a disorder average, which strongly diminishes the influence of the particular Monte Carlo dynamics.
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    • note
    • We shall need to recall the main features of the Swendsen-Wang dynamics, as formulated in Ref. The configuration space is expanded; to the original spins { S x } in the lattice sites, we add bond variables b x y =0,1 in the lattice bonds joining nearest-neighbor sites x and y (the marginal probability for the spins is the Boltzmann weight of the original Ising model). The b=1 bonds are said to be occupied. Two lattice sites connected by a chain of occupied bonds are said to belong to the same cluster. The clusters partition the lattice into connected components. A crucial role is played by the conditional probabilities. That of the spins, given the bonds is: all the spins in a cluster take the same value, the spin values in different clusters are statistically independent and equal ±1 with 50% probability. For that of the bonds, given the spins, different bonds are statistically independent, and a given bond can be one only if it connects spins of equal sign and, in that case, with probability 1- e-2κ. The two Schrödinger-type operators, Pspin and Pbond belong to the heat-bath category; Pspin (Pbond) leave the bonds (spins) unchanged and choose the new spin (bond) configuration according to the conditional probability of the spins (bonds), given the bonds (spins). As all heat-bath dynamics, both Pbond and Pspin verify detailed balance. Their product PSW = Pspin Pbond verifies only the softer balance condition, Eq. 10.
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    • Combining ηCt ηSt =0 with Eqs. 3 8 9 10, we recover the well-known cluster estimator for U4: U4 = 3 (□c nc2) 2 -2 □c nc4 □ □c nc2 □ 2.
    • Combining ηCt ηSt □ =0 with Eqs. 3 8 9 10, we recover the well-known cluster estimator for U4: U4 = 3 (□c nc2) 2 -2 □c nc4 □ □c nc2 □ 2.
  • 30
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    • For finite L, gC >0 while the large- L limit for U4 is 3.
    • For finite L, gC >0 while the large- L limit for U4 is 3.
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    • For instance, M2 □ = Pspin M2 □ = C□. A telegraphic proof of CC BSW (0) =0 is also obtained by combining C M2 □ = Pspin C M2 □ with Pspin C M2 =C Pspin M2 = C2 and with Eq. 18.
    • For instance, M2 □ = Pspin M2 □ = C□. A telegraphic proof of CC BSW (0) =0 is also obtained by combining C M2 □ = Pspin C M2 □ with Pspin C M2 =C Pspin M2 = C2 and with Eq. 18.
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* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.