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  • 1
    Electronic Resource
    Electronic Resource
    A new proof of the existence and nontriviality of the continuum ϕ 2 4 and ϕ 3 4 quantum field theories (1983)
    Springer
    Communications in mathematical physics 91 (1983), S. 141-186 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We use Schwinger-Dyson equations combined with rigorous “perturbation-theoretic” correlation inequalities to give a new and extremely simple proof of the existence and nontriviality of the weakly-coupled continuum ϕ 2 4 and ϕ 3 4 quantum field theories, constructed as subsequence limits of lattice theories. We prove an asymptotic expansion to order λ or λ2 for the correlation functions and for the mass gap. All Osterwalder-Schrader axioms are satisfied except perhaps Euclidean (rotation) invariance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01211157
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  • 2
    Electronic Resource
    Electronic Resource
    More surprises in the general theory of lattice systems (1982)
    Springer
    Communications in mathematical physics 86 (1982), S. 327-336 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract I use Israel's methods to prove new theorems of “ubiquitous pathology” for classical and quantum lattice systems. The main result is the following: Let Φ be any interaction and ϱ be any translation-invariant equilibrium state for Φ (extremal or not). Then there exists a sequence {Φ k } of interactions converging to Φ, having extremal (or even unique) translation-invariant equilibrium states ϱ k , such that {ϱ k } converges to ϱ. In certain situations the perturbations Φ k −Φ can be chosen to lie in a cone of “antiferromagnetic pair interactions.” I discuss the connection with results of Daniëls and van Enter, and point out an application to the one-dimensional ferromagnetic Ising model with 1/r 2 interaction (Thouless effect).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01212172
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  • 3
    Electronic Resource
    Electronic Resource
    The random-walk representation of classical spin systems and correlation inequalities (1983)
    Springer
    Communications in mathematical physics 91 (1983), S. 117-139 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We use the random-walk representation to prove the first few of a new family of correlation inequalities for ferromagnetic ϕ4 lattice models. These inequalities state that the finite partial sums of the propagator-resummed perturbation expansion for the 4-point function form an alternating set of rigorous upper and lower bounds for the exact 4-point function. Generalizations to 2n-point functions are also given. A simple construction of the continuum ϕ d 4 quantum field theory (d〈4), based on these inequalities, is described in a companion paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01206055
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  • 4
    Electronic Resource
    Electronic Resource
    A general Lee-Yang theorem for one-component and multicomponent ferromagnets (1981)
    Springer
    Communications in mathematical physics 80 (1981), S. 153-179 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We show that any measure on ℝ n possessing the Lee-Yang property retains that property when multiplied by a ferromagnetic pair interaction. Newman's Lee-Yang theorem for one-component ferromagnets with general single-spin measure is an immediate consequence. We also prove an analogous result for two-component ferromagnets. ForN-component ferromagnets (N ≧ 3), we prove a Lee-Yang theorem when the interaction is sufficiently anisotropic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01213009
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  • 5
    Electronic Resource
    Electronic Resource
    Existence of compatible families of proper regular conditional probabilities (1981)
    Springer
    Probability theory and related fields 56 (1981), S. 537-548 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Let (Ω, ℱ, μ) be a perfect probability space with ℱ countably generated, and let IB be a family of sub-σ-fields of ℱ. Under a countability condition on the family IB, I show that there exists a family {π∇}∇∈IB of regular conditional probabilities which are everywhere compatible. Under a more stringent condition on IB, I show that the π ∇ can furthermore be chosen to be everywhere proper. It follows that in the Dobrushin-Lanford-Ruelle formulation of the statistical mechanics of classical lattice systems, every (perfect) probability measure is a Gibbs measure for some specification.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00531432
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  • 6
    Electronic Resource
    Electronic Resource
    Rigorous proof of the high-temperature Josephson inequality for critical exponents (1981)
    Springer
    Journal of statistical physics 25 (1981), S. 51-56 
    Details
    ISSN: 1572-9613
    Keywords: Josephson inequality ; critical exponents ; correlation inequalities ; hyperscaling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract I give a rigorous proof of the high-temperature Josephson inequalitydv ⩾ 2−α, following the original ideas of Josephson. The proof is applicable to a class of models including the ferromagnetic Ising model and theϕ 4 lattice field theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01008478
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  • 7
    Electronic Resource
    Electronic Resource
    More inequalities for critical exponents (1981)
    Springer
    Journal of statistical physics 25 (1981), S. 25-50 
    Details
    ISSN: 1572-9613
    Keywords: Critical exponents ; critical-exponent inequalities ; correlation inequalities ; Josephson inequality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv′ ⩾γ′+2β ⩾ 2−α′. Others are 1 ⩽γ′ ⩽ 1 +v′φ, 1 ⩽ζ ⩽ 1δμ φ,δ ⩾ 1,dμφ ⩾ 1 + 1/δ (for φ ⩾d),dv′φ, ⩾ Δ′3 + α (for φ ⩾d), Δ4 ⩾γ, and Δ2m ⩽ Δ2m+2 (form ⩾ 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01008477
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  • 8
    Electronic Resource
    Electronic Resource
    Rigorous entropy-energy arguments (1981)
    Springer
    Journal of statistical physics 25 (1981), S. 679-694 
    Details
    ISSN: 1572-9613
    Keywords: Entropy ; phase transitions ; Ising model ; plane rotor ; spin systems ; one-dimensional models ; two-dimensional models ; symmetry breaking ; Thouless effect
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a method for making rigorous various arguments which predict that certain situations are unstable because of a balance of energy vs. entropy. As applications, we give yet another proof that the two-dimensional plane rotor has no spontaneous magnetization and we make rigorous Thouless' arguments on the one-dimensional Ising model with couplingJ/n 2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01022362
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  • 9
    Electronic Resource
    Electronic Resource
    New Monte Carlo method for the self-avoiding walk (1985)
    Springer
    Journal of statistical physics 40 (1985), S. 483-531 
    Details
    ISSN: 1572-9613
    Keywords: Self-avoiding walk ; polymer ; lattice model ; critical exponents ; Monte Carlo ; algorithm ; maximum-likelihood estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We findμ=2.63820 ± 0.00004 ± 0.00030γ=1.352 ± 0.006 ± 0.025νv=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length ≈ 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01017183
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  • 10
    Electronic Resource
    Electronic Resource
    Rigorous entropy-energy arguments (1982)
    Springer
    Journal of statistical physics 29 (1982), S. 155-155 
    Details
    ISSN: 1572-9613
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01008255
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