1989 Fiscal Year Final Research Report Summary
Theoretical Research of Exotic Phase Transitions
| Project/Area Number |
63460035
|
|---|
| Research Category |
Grant-in-Aid for General Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
物性一般（含極低温･固体物性に対する理論）
|
|---|
| Research Institution | University of Tokyo |
|---|
Principal Investigator |
SUZUKI Masuo Univ. of Tokyo, Dept. of Phys, Professor, 理学部, 教授 (80013473)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KATORI Makoto Univ. of Tokyo, Dept. of Phys, Research Associate, 理学部, 助手 (60202016)
MIYASHITA Seiji Kyoto Univ, College-Liberal Arts, Associate Professor, 教養部, 助教授 (10143372)
|
|---|
| Project Period (FY) |
1988 – 1989
|
| Keywords | Phase Transition / Critical Phenomena / Coherent-Anomaly Method / Spin Glass / Chiral Order / Effective Field Theory / Decomposition Formula / Fractal Path Integrals |
|---|
| Research Abstract |
The research project "Theoretical Research of Exotic Phase Transitions" was performed by the support of the Grant-in-Aid from the Ministry of Education, Science and Culture during two fiscal years from april 1988.
A general theory of phase transitions, so-called the coherent-anomaly method (CAM) and the super-effective-field theory have been developed to study exotic phase transitions such as spin glasses and chiral orders. It has been shown that there exists no phase transition in the two-dimensional <plus-minus>J Ising spin glass model, but that there exists a phase transition in three dimensions for the same model. The critical point T_<**> and the nonlinear susceptibility exponent gamma_* have been estimated as T_<**> <similar or equal> 1.4J/k_B and gamma_* <similar or equal> 3. Concerning the scalar chital order, it has been found, using the super-effective-field theory, to be quite difficult to occur in the two-dimensional antiferromagnetic Heisenberg model with cross bonds on a s
… More
quare lattice. This result agrees with other numerical studies.
Suzuki has discovered a new scheme of "fractal path integrals". This is based on the following general decomposition theorem (Suzuki): e^<x(A+B)> = e^<t1A>e^<t2B>e^<t3A>e^<t4B>...e^<tNA> + O(x^<m+1>), for any positive integer m, where {t_j} are all real numbers proportional to x and they are fractal in their distribution. This new scheme including negative time or temperature is also conceptually interesting and it will be applicable to field theory and nuclear physics. In particular, this mew scheme of fractal decomposition of exponential operators is useful in quantum Monte Carlo simulations, if we combine this new approximant with the Trotter formula, because the resultant error becomes of the order of x^<m+1>n^<-m> for the Trotter number n.
In order to make effective use of the CAM theory, Suzuki has devised the multi-effective- field theory and the confluent-transfer matrix method. The combination of the CAM theory with the former has given the estimate gamma <similar or equal> 1.7498 for the two-dimensional Ising m Less
|
