{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"critpt","formal_name":"CritPt","introduction":"研究水準の物理問題で、科学的理解と多段階の推論・計算を評価するベンチマークです。公開データには70の課題があり、問題文とコード雛形を組み合わせて解答を構成します。\n\nCritPt evaluates scientific understanding and multi-step reasoning and computation on research-level physics problems. Its public dataset contains 70 challenges with problem descriptions and code templates.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://critpt.com/","indexing_mode":"noindex"},"task_id":"43549b5b-12fb-5540-8faf-06bf7ba110a0","task_key":"train--Challenge~5f11~5fmain","task_revision_id":"1","upstream_id":"Challenge_11_main","short_description":"Consider a (1+1)-D Lagrangian that consists of a Majorana fermion $\\chi$ and…","config":"","split":"train","body":"{\"code_template\":\"import sympy as sp\\n\\nDelta, x, K, m = sp.symbols('Delta x K m')\\n\\ndef answer(Delta, x, K, m):\\n    r\\\"\\\"\\\"\\n    Return the expressions of the beta functions in Sympy format.\\n\\n    Inputs\\n    ----------\\n    Delta: sympy.Symbol, coupling constant $\\\\Delta$\\n    x: sympy.Symbol, scaling dimension of $\\\\Delta$, $x\\\\equiv [\\\\Delta]$\\n    K: sympy.Symbol, parameter $K$\\n    m: sympy.Symbol, parameter $m$\\n\\n    Outputs\\n    ----------\\n    beta_Delta: sympy.Expr, beta function for coupling constant $\\\\Delta$, $\\\\beta(\\\\Delta)$\\n    beta_x: sympy.Expr, beta function for $x$, $\\\\beta(x)$\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    beta_Delta = ...  # a SymPy expression of inputs\\n    beta_x = ...      # a SymPy expression of inputs\\n    # ---------------------------------------------------------------\\n\\n    return beta_Delta, beta_x\",\"problem_description\":\"\\n\\n# Problem setup:\\nConsider a (1+1)-D Lagrangian that consists of a Majorana fermion $\\\\chi$ and boson $\\\\phi$ with compactification radius $\\\\sqrt{\\\\frac{K}{m}}$:\\n\\n$\\\\\\\\\\nL=\\\\frac{i}{2}\\\\bar{\\\\chi}\\\\not\\\\!{\\\\partial}\\\\chi+\\\\frac{m}{2\\\\pi K}(\\\\partial_\\\\mu \\\\phi)^2+\\\\frac{\\\\Delta}{2}i\\\\bar{\\\\chi}\\\\chi\\\\cos(2m\\\\phi).\\\\\\\\\\n$\\n\\nIn this problem, $x\\\\equiv [\\\\Delta]$, where $[\\\\Delta]$ is the scaling dimension of the coupling constant $\\\\Delta$\\n\\n# Main problem:\\n\\nFind the beta functions for coupling constants $\\\\Delta$ and $x$ at one-loop level, with the convention that a positive beta function means that the\\nsystem flows to strong coupling in the IR.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}