Kosterlitz-Thouless Phase Transition of the ANNNI model in Two Dimensions

The spin structure of an axial next-nearest-neighbor Ising (ANNNI) model in two dimensions (2D) is a renewed problem because different Monte Carlo (MC) simulation methods predicted different spin orderings. The usual equilibrium simulation predicts the occurrence of a floating incommensurate (IC) Kosterlitz-Thouless (KT) type phase, which never emerges in non-equilibrium relaxation (NER) simulations. In this paper, we first examine previously published results of both methods, and then investigate a higher transition temperature, $T_{c1}$, between the IC and paramagnetic phases. In the usual equilibrium simulation, we calculate the layer magnetization on larger lattices (up to $512 \times 512$ sites) and estimate $T_{c1} \approx 1.16J$ with frustration ratio $\kappa (\equiv -J_2/J_1) = 0.6$. We examine the nature of the phase transition in terms of the Binder ratio $g_L$ of spin overlap functions and the correlation-length ratio $\xi/L$. In the NER simulation, we observe the spin dynamics in equilibrium states by means of an autocorrelation function, and also observe the layer magnetization relaxations from the ground and disordered states. These quantities exhibit an algebraic decay at $T \lesssim 1.17J$. We conclude that the two-dimensional ANNNI model actually admits an IC phase transition of the KT type.Comment: 20 pages, 16 figure

Cluster Heat Bath Algorithm in Monte Carlo Simulations of Ising Models

We have proposed a cluster heat bath method in Monte Carlo simulations of Ising models in which one of the possible spin configurations of a cluster is selected in accordance with its Boltzmann weight. We have argued that the method improves slow relaxation in complex systems and demonstrated it in an axial next-nearest-neighbor Ising(ANNNI) model in two-dimensions.Comment: 10 pages, REVTeX, 2 figures, to appear in Phys.Rev.Let

Three Dimensional Heisenberg Spin Glass Models with and without Random Anisotropy

We reexamine the spin glass (SG) phase transition of the $\pm J$ Heisenberg models with and without the random anisotropy $D$ in three dimensions ($d = 3$) using complementary two methods, i.e., (i) the defect energy method and (ii) the Monte Carlo method. We reveal that the conventional defect energy method is not convincing and propose a new method which considers the stiffness of the lattice itself. Using the method, we show that the stiffness exponent $\theta$ has a positive value ($\theta > 0$) even when $D = 0$. Considering the stiffness at finite temperatures, we obtain the SG phase transition temperature of $T_{\rm SG} \sim 0.19J$ for $D = 0$. On the other hand, a large scale MC simulation shows that, in contrary to the previous results, a scaling plot of the SG susceptibility $\chi_{\rm SG}$ for $D = 0$ is obtained using almost the same transiton temperature of $T_{\rm SG} \sim 0.18J$. Hence we believe that the SG phase transition occurs in the Heisenberg SG model in $d = 3$.Comment: 15 pages, 9 figures, to be published in J. Phys.

Development of Drug-loaded Nanoparticles for Targeted Chemotherapy.

Cancer is the second highest cause of death in the US, and chemotherapy is one of the common cancer therapies. In order to reduce side effects and avoid cancer’s resistance to antitumor drugs, we use nanoparticle (NP)-assisted chemotherapy. This strategy can selectively deliver high concentrations of antitumor drugs to the tumor area, because NPs can encapsulate antitumor drugs, target the tumor area by active and passive targeting mechanisms, and release the drugs inside the cancer cells. This work focuses on three aspects of such NPs: high loading with antitumor drugs, controlled release of antitumor drugs, and high cellular uptake by the NPs. As a model system, polyacrylamide-based NPs were loaded with cisplatin. The effects of functional groups in the NPs, and the effects of matrix densities, were evaluated in terms of the NPs’ drug-loading, their release profile, and their cellular uptake. The carboxyl-functionalized NPs achieved 2 times higher loading and faster release of cisplatin than the amine-functionalized NPs. In contrast, the amine-functionalized NPs had 3.5 times better cellular uptake than the carboxyl-functionalized NPs. Tuning the matrix density of those NPs could control the release of cisplatin. Also, cisplatin-loaded, temperature-responsive NPs were synthesized so as to incorporate a trigger for cisplatin release in the cancer cells. The elevated temperature successfully enhanced the release of cisplatin from the synthesized NPs, especially under acidic conditions simulating lysosomes, which were the destination of the NPs inside the cells. Also, the in vitro cytotoxicity of the NPs is accelerated at high temperature. Finally, polyethylenimine (PEI) was incorporated into cisplatin-loaded PAA-NPs. Incorporation of PEI enhanced the cellular uptake of the PAA NPs 7 times, and resulted in significantly higher cytotoxicity. Other properties of these NPs, such as enhanced loading, enhanced release, and endosomal escape may contribute to their higher cytotoxicity. These results confirmed the importance of the following three factors when designing NPs for NP-assisted chemotherapy: (1) high loading with antitumor drugs, (2) controlled release of antitumor drugs, and (3) high cellular uptake of the NPs.PhDBiophysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111622/1/tshira_1.pd

Parisi States in a Heisenberg Spin-Glass Model in Three Dimensions

We have studied low-lying metastable states of the $\pm J$ Heisenberg model in two ($d=2$) and three ($d=3$) dimensions having developed a hybrid genetic algorithm. We have found a strong evidence of the occurrence of the Parisi states in $d=3$ but not in $d=2$. That is, in $L^d$ lattices, there exist metastable states with a finite excitation energy of $\Delta E \sim O(J)$ for $L \to \infty$, and energy barriers $\Delta W$ between the ground state and those metastable states are $\Delta W \sim O(JL^{\theta})$ with $\theta > 0$ in $d=3$ but with $\theta < 0$ in $d=2$. We have also found droplet-like excitations, suggesting a mixed scenario of the replica-symmetry-breaking picture and the droplet picture recently speculated in the Ising SG model.Comment: 4 pages, 6 figure