Correlation length bounds for disordered Ising ferromagnets

Thed-dimensional, nearest-neighbor disordered Ising ferromagnet: $$H = - \sum {J_{ij} \sigma _i \sigma _j }$$ is studied as a function of both temperature,T, and a disorder parameter,λ, which measures the size of fluctuations of couplingsJ _ij ≧0. A finite-size scaling correlation length,ζ _f (T, λ), is defined in terms of the magnetic response of finite samples. This correlation length is shown to be equivalent, in the scaling sense, to the quenched average correlation lengthζ(T, λ), defined as the asymptotic decay rate of the quenched average two-point function. Furthermore, the magnetic response criterion which definesζ _f is shown to have a scale-invariant property at the critical point. The above results enable us to prove that the quenched correlation length satisfies: $$C\left| {\log \xi (T)} \right|\xi (T) \geqq \left| {T - T_c } \right|^{ - {2 \mathord{\left/ {\vphantom {2 d}} \right. \kern-\nulldelimiterspace} d}}$$ which implies the boundv≧2/d for the quenched correlation length exponent.     

First-order transitions in spherical models: Finite-size scaling

Finite-size behavior near the first-order phase boundary of ferromagnetic spherical models is investigated for block- and cylinder-shaped systems ind dimensions. The bulk thermodynamic singularities are rounded and, asymptotically for large size, obey appropriate scaling laws. Both short-range interactions and long-range couplings, decaying like 1/r^d+ with >0, are analyzed: the short-range results agree precisely with a recently developed scaling theory forO(n) symmetric systems in the limitn. More generally, the scaling functions are universal, depending only on . Explicit aspects of the shape and interactions enter only in the spin wave or Goldstone mode contributions which appear, technically, as corrections to scaling. An appendix analyzes the truncation error in the approximation, by many-fold sums, of multivariate integrals with integrands diverging like [_ja_{j j} ² ]^- as 0.     

Simultaneous Two-Photon Activation of Type-I Photodynamic Therapy Agents

The excitation and emission properties of several psoralen derivatives are compared using conventional single-photon excitation and simultaneous two-photon excitation (TPE). Two-photon excitation is effected using the output of a mode-locked titanium: sapphire laser, the near infrared output of which is used to promote non-resonant TPE directly. Specifically, the excitation spectra and excited-state properties of 8-methoxypsoralen and 4′-aminomethyl-4,5,8-trimethylpsoralen are shown to be equivalent using both modes of excitation. Further, in vitro feasibility of two-photon photodynamic therapy (PDT) is demonstrated using Salmonella typhimurium. Two-photon excitation may be beneficial in the practice of PDT because it would allow replacement of visible or UV excitation light with highly penetrating, nondamag-ing near infrared light and could provide a means for improving localization of therapy. Comparison of possible laser excitation sources for PDT reveals the titanium: sapphire laser to be exceptionally well suited for nonlinear excitation of PDT agents in biological systems due to its extremely short pulse width and high repetition rate that together provide efficient PDT activation and greatly reduced potential for biological damage     

Conductance of aqueous NaCl solutions at pressures up to 2000 atm

Electrical conductance measurements are reported for aqueous NaCl solutions at 25°C as a function of concentration up to 0.02M and pressures up to 2000 atm. The data were analyzed with the Fuoss-Hsia-Fernandez-Prini (FHFP) equation. The standard error of fit, , varies from 0.04 at 1 atm to 0.10 at 2000 atm. The increase of with pressure arises from increasing non-randomness in the distribution of errors about the FHFP equation suggesting that modifications in the theory are necessary. The pressure dependence of _O for NaCl and KCl is nearly identical.Contribution of the Scripps Institution of Oceanography, New Series