Convergence and stability of the renormalisation group

Within the exact renormalisation group approach, it is shown that stability properties of the flow are controlled by the choice for the regulator. Equally, the convergence of the flow is enhanced for specific optimised choices for the regularisation. As an illustration, we exemplify our reasoning for 3d scalar theories at criticality. Implications for other theories are discussed.Within the exact renormalisation group approach, it is shown that stability properties of the flow are controlled by the choice for the regulator. Equally, the convergence of the flow is enhanced for specific optimised choices for the regularisation. As an illustration, we exemplify our reasoning for 3d scalar theories at criticality. Implications for other theories are discussed.Within the exact renormalisation group approach, it is shown that stability properties of the flow are controlled by the choice for the regulator. Equally, the convergence of the flow is enhanced for specific optimised choices for the regularisation. As an illustration, we exemplify our reasoning for 3d scalar theories at criticality. Implications for other theories are discussed.Within the exact renormalisation group approach, it is shown that stability properties of the flow are controlled by the choice for the regulator. Equally, the convergence of the flow is enhanced for specific optimised choices for the regularisation. As an illustration, we exemplify our reasoning for $3d$ scalar theories at criticality. Implications for other theories are discussed