In three-dimensional O( N ) models, we investigate the low-momentum behavior of the two-point Green's function G ( x ) in the critical region of the symmetric phase. We consider physical systems whose criticality is characterized by a rotational-invariant fixed point. In non-rotational invariant physical systems with O( N )-invariant interactions, the vanishing of space-anisotropy approaching the rotational-invariant fixed point is described by a critical exponent ρ, which is universal and is related to the leading irrelevant operator breaking rotational invariance. At N = ∞ one finds ρ = 2. We show that, for all values of N ⩾ 0, ρ ≃ 2. Non-Gaussian corrections to the universal low-momentum behavior of G ( x ) are evaluated, and found to be very small.In three-dimensional O( N ) models, we investigate the low-momentum behavior of the two-point Green's function G ( x ) in the critical region of the symmetric phase. We consider physical systems whose criticality is characterized by a rotational-invariant fixed point. In non-rotational invariant physical systems with O( N )-invariant interactions, the vanishing of space-anisotropy approaching the rotational-invariant fixed point is described by a critical exponent ρ, which is universal and is related to the leading irrelevant operator breaking rotational invariance. At N = ∞ one finds ρ = 2. We show that, for all values of N ⩾ 0, ρ ≃ 2. Non-Gaussian corrections to the universal low-momentum behavior of G ( x ) are evaluated, and found to be very small.

arXiv:cond-mat/9612164Europhysics Letters (EPL)Jun 10, 199719 citations

Transformation Under Rotations

Igal Talmi

The shell model Hamiltonian is invariant under spatial rotations. This fact has profound implications for its eigenstates. Other physical operators which are not invariant may have well defined transformation properties under rotations. Much of the following is related to the behavior of various physical entities, operators as well as wave functions, under rotations in three-dimensional space. In the following pages a simple introduction to this subject is presented. First, single particle states and operators will be discussed. Subsequent sections will deal with transformation properties of more general systems of several nucleons.The shell model Hamiltonian is invariant under spatial rotations. This fact has profound implications for its eigenstates. Other physical operators which are not invariant may have well defined transformation properties under rotations. Much of the following is related to the behavior of various physical entities, operators as well as wave functions, under rotations in three-dimensional space. In the following pages a simple introduction to this subject is presented. First, single particle states and operators will be discussed. Subsequent sections will deal with transformation properties of more general systems of several nucleons.

Routledge eBooksOct 6, 20170 citations

On transformations of physical systems

Lazar Mayants

Foundations of PhysicsOct 1, 19763 citations

Two-point correlation function of three-dimensional O(N) models: The critical limit and anisotropy

Massimo Campostrini B, Andrea Pelissetto C, Paolo Rossi +1 more

In three-dimensional $O(N)$ models, we investigate the low-momentum behavior of the two-point Green's function $G(x)$ in the critical region of the symmetric phase. We consider physical systems whose criticality is characterized by a rotationally invariant fixed point. Several approaches are exploited, such as strong-coupling expansion of lattice $N$ -vector model, and $1/N$ expansion, field-theoretical methods within the ${\ensuremath{\varphi}}^{4}$ continuum formulation. Non-Gaussian corrections to the universal low-momentum behavior of $G(x)$ are evaluated, and found to be very small. In nonrotationally invariant physical systems with $O(N)$ -invariant interactions, the vanishing of the spatial anisotropy approaching the rotationally invariant fixed point is described by a critical exponent $\ensuremath{\rho}$, which is universal and is related to the leading irrelevant operator breaking rotational invariance. At $N=\ensuremath{\infty}$ one finds $\ensuremath{\rho}=2$. We show that, for all values of $N>~0$ , $\ensuremath{\rho}\ensuremath{\simeq}2$.In three-dimensional $O(N)$ models, we investigate the low-momentum behavior of the two-point Green's function $G(x)$ in the critical region of the symmetric phase. We consider physical systems whose criticality is characterized by a rotationally invariant fixed point. Several approaches are exploited, such as strong-coupling expansion of lattice $N$-vector model, and $1/N$ expansion, field-theoretical methods within the ${\ensuremath{\varphi}}^{4}$ continuum formulation. Non-Gaussian corrections to the universal low-momentum behavior of $G(x)$ are evaluated, and found to be very small. In nonrotationally invariant physical systems with $O(N)$-invariant interactions, the vanishing of the spatial anisotropy approaching the rotationally invariant fixed point is described by a critical exponent $\ensuremath{\rho}$, which is universal and is related to the leading irrelevant operator breaking rotational invariance. At $N=\ensuremath{\infty}$ one finds $\ensuremath{\rho}=2$. We show that, for all values of $N>~0$, $\ensuremath{\rho}\ensuremath{\simeq}2$.

arXiv:cond-mat/9705086Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJan 1, 199874 citations

In three-dimensional

O(N)

models, we investigate the low-momentum behavior of the two-point Green's function

G(x)

in the critical region of the symmetric phase. We consider physical systems whose criticality is characterized by a rotationally invariant fixed point. Several approaches are exploited, such as strong-coupling expansion of lattice

N

-vector model, and

1/N

expansion, field-theoretical methods within the ${\ensuremath{\varphi}}^{4}$ continuum formulation. Non-Gaussian corrections to the universal low-momentum behavior of

G(x)

are evaluated, and found to be very small. In nonrotationally invariant physical systems with

O(N)

-invariant interactions, the vanishing of the spatial anisotropy approaching the rotationally invariant fixed point is described by a critical exponent $\ensuremath{\rho}$, which is universal and is related to the leading irrelevant operator breaking rotational invariance. At $N=\ensuremath{\infty}$ one finds $\ensuremath{\rho}=2$. We show that, for all values of

N>~0

, $\ensuremath{\rho}\ensuremath{\simeq}2$.