# Fingerprint Dive into the research topics where Takashi Hara is active. These topic labels come from the works of this person. Together they form a unique fingerprint.

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### Mathematics

Self-avoiding Walk

Lace Expansion

Critical Behavior

Mean Field

Higher Dimensions

Critical Exponents

Scaling Limit

Spin Systems

Critical point

Nearest Neighbor

High-dimensional

Lattice Animals

Correlation Length

Brownian Excursion

Critical Phenomena

Susceptibility

Model

Triangle

Simple Random Walk

Critical Dimension

Logarithmic

Renormalization Group

Lower bound

P-adic

Animals

Iwasawa Theory

Ising Model

Decay of Correlations

Convergence in Distribution

Trajectory

Generating Function

Lattice System

Ferromagnet

Asymptotically Linear

Hierarchical Model

Skeleton

Riemann zeta function

Exponent

Mean Square

Brownian motion

Polymers

Fixed point

Logarithm

Magnetization

Hilbert Modular Forms

Two Dimensions

Exact Enumeration

Galois Extension

Infrared

Imply

### Physics & Astronomy

#### General

exponents

expansion

critical point

scaling

Ising model

triangles

enumeration

#### Engineering

magnetic permeability

interlayers

#### Aeronautics

trajectory control

trajectories

#### Aerospace Sciences

gravitational collapse

#### Life Sciences

musculoskeletal system

animals

#### Chemistry and Materials

polymers

nitrogen

#### Mathematical and Computer Sciences

theorems

#### Physics

perturbation